NTU Scholarshttps://scholars.lib.ntu.edu.twThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 07 Feb 2023 09:04:53 GMT2023-02-07T09:04:53Z50301- Lattice points counting via Einstein metricshttps://scholars.lib.ntu.edu.tw/handle/123456789/369395Title: Lattice points counting via Einstein metrics
Sun, 01 Jan 2012 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3693952012-01-01T00:00:00Z
- Motivic and quantum invariance under stratified Mukai flowshttps://scholars.lib.ntu.edu.tw/handle/123456789/31532Title: Motivic and quantum invariance under stratified Mukai flows
Authors: Fu, B. H.; Wang, C. L.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/315322008-01-01T00:00:00Z
- Estimate of the conformal scalar curvature equation via the method of moving planes. IIhttps://scholars.lib.ntu.edu.tw/handle/123456789/338021Title: Estimate of the conformal scalar curvature equation via the method of moving planes. II
Authors: Chen, C.-C.; Lin, C.-S.; CHANG-SHOU LIN
Thu, 01 Jan 1998 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3380211998-01-01T00:00:00Z
- On the σ2-scalar curvaturehttps://scholars.lib.ntu.edu.tw/handle/123456789/355918Title: On the σ2-scalar curvature
Authors: Ge, Y.; Lin, C.-S.; Wang, G.; CHANG-SHOU LIN
Fri, 01 Jan 2010 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3559182010-01-01T00:00:00Z
- Estimate of the conformal scalar curvature equation via the method of moving planes. IIhttps://scholars.lib.ntu.edu.tw/handle/123456789/337675Title: Estimate of the conformal scalar curvature equation via the method of moving planes. II
Authors: Chen, C.-C.; Lin, C.-S.; CHIUN-CHUAN CHEN
Thu, 01 Jan 1998 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3376751998-01-01T00:00:00Z
- Hitchin's Connection and Differential Operators with Values in the Determinant Bundlehttps://scholars.lib.ntu.edu.tw/handle/123456789/31154Title: Hitchin's Connection and Differential Operators with Values in the Determinant Bundle
Authors: Sun, Xiaotao; Tsai, I-Hsun
Abstract: For a family of smooth curves, we have the associated family of moduli spaces of stable bundles with fixed determinant on the curves. There exists a so-called theta line bundle on the family of moduli spaces. When the Kodaira–Spencer map of the family of curves is an isomorphism, we prove in this paper an identification theorem between sheaves of differential operators on the theta line bundle and higher direct images of vector bundles on curves. As an application, the so-called Hitchin connection on the direct image of (powers of) the theta line bundle is derived naturally from the identification theorem. A logarithmic extension to certain singular stable curves is also presented in this paper. © 2003 Applied Probability Trust.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/311542004-01-01T00:00:00Z
- The local isometric embedding in R<sup>3</sup> of 2-dimensional riemannian manifolds with nonnegative curvaturehttps://scholars.lib.ntu.edu.tw/handle/123456789/318300Title: The local isometric embedding in R<sup>3</sup> of 2-dimensional riemannian manifolds with nonnegative curvature
Authors: Lin, C.-S.; CHANG-SHOU LIN
Tue, 01 Jan 1985 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3183001985-01-01T00:00:00Z
- Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifoldhttps://scholars.lib.ntu.edu.tw/handle/123456789/31587Title: Li-Yau gradient estimate and entropy formulae for the CR heat equation in a closed pseudohermitian 3-manifold
Authors: Chang, Shu-Cheng; Kuo, Ting-Jung; Lai, Sin-Hua
Sat, 01 Jan 2011 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/315872011-01-01T00:00:00Z
- Self-similar solutions and translating solitons for Lagrangian mean curvature flowhttps://scholars.lib.ntu.edu.tw/handle/123456789/31063Title: Self-similar solutions and translating solitons for Lagrangian mean curvature flow
Authors: Dominic J.; Lee, Y.-I.; YNG-ING LEE; MAO-PEI TSUI
Tue, 01 Jan 2008 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/310632008-01-01T00:00:00Z
- Local isometric embedding of surfaces with nonpositive Gaussian curvaturehttps://scholars.lib.ntu.edu.tw/handle/123456789/301550Title: Local isometric embedding of surfaces with nonpositive Gaussian curvature
Authors: Han, Q.; Hong, J.-X.; Lin, C.-S.; CHANG-SHOU LIN
Wed, 01 Jan 2003 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3015502003-01-01T00:00:00Z
- Ancient solutions of the affine normal flowhttps://scholars.lib.ntu.edu.tw/handle/123456789/338006Title: Ancient solutions of the affine normal flow
Authors: Loftin, J.; Tsui, M.-P.; MAO-PEI TSUI
Tue, 01 Jan 2008 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3380062008-01-01T00:00:00Z
- Cohomology and Hodge theory on symplectic manifolds: IIIhttps://scholars.lib.ntu.edu.tw/handle/123456789/31821Title: Cohomology and Hodge theory on symplectic manifolds: III
Authors: CHUNG-JUN TSAI; Tseng, L.-S.; Yau, S.-T.
Abstract: We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Papers I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered cohomologies give a two-sided resolution of Lefschetz maps, and thereby, they are directly related to the kernels and cokernels of the Lefschetz maps. We also introduce a novel, non-associative product operation on differential forms for symplectic manifolds. This product generates an A∞-algebra structure on forms that underlies the filtered cohomologies and gives them a ring structure. As an application, we demonstrate how the ring structure of the filtered cohomologies can distinguish different symplectic four-manifolds in the context of a circle times a fibered three-manifold.
Mon, 03 Feb 2014 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/318212014-02-03T00:00:00Z
- Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifoldhttps://scholars.lib.ntu.edu.tw/handle/123456789/362622Title: Li-yau gradient estimate and entropy formulae for the cr heat equation in a closed pseudohermitian 3-manifold
Authors: Chang, S.-C.; Kuo, T.-J.; Lai, S.-H.; SHU-CHENG CHANG
Sat, 01 Jan 2011 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3626222011-01-01T00:00:00Z
- Self-similar solutions and translating solitons for Lagrangian mean curvature flowhttps://scholars.lib.ntu.edu.tw/handle/123456789/355906Title: Self-similar solutions and translating solitons for Lagrangian mean curvature flow
Authors: Joyce, D.; Lee, Y.-I.; Tsui, M.-P.; MAO-PEI TSUI
Fri, 01 Jan 2010 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3559062010-01-01T00:00:00Z
- Prescribing scalar curvature on SN, Part 1: Apriori estimateshttps://scholars.lib.ntu.edu.tw/handle/123456789/292025Title: Prescribing scalar curvature on SN, Part 1: Apriori estimates
Authors: Chen, C.-C.; CHIUN-CHUAN CHEN; CHANG-SHOU LIN
Mon, 01 Jan 2001 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/2920252001-01-01T00:00:00Z
- Cohomology theory in birational geometryhttps://scholars.lib.ntu.edu.tw/handle/123456789/296675Title: Cohomology theory in birational geometry
Authors: Wang, C.-L.; CHIN-LUNG WANG
Tue, 01 Jan 2002 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/2966752002-01-01T00:00:00Z
- Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flowshttps://scholars.lib.ntu.edu.tw/handle/123456789/31066Title: Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows
Authors: Lee, Y.I.; Wang, M.T.; LeeYI
Mon, 01 Jan 2007 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/310662007-01-01T00:00:00Z
- Explicit birational geometry of 3-folds of general type, IIhttps://scholars.lib.ntu.edu.tw/handle/123456789/355898Title: Explicit birational geometry of 3-folds of general type, II
Authors: Chen, J.A.; Chen, M.; JUNG-KAI CHEN
Fri, 01 Jan 2010 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3558982010-01-01T00:00:00Z
- Calabi-yau theorem and hodge-laplacian heat equation in a closed strictly pseudoconvex CR manifoldhttps://scholars.lib.ntu.edu.tw/handle/123456789/384871Title: Calabi-yau theorem and hodge-laplacian heat equation in a closed strictly pseudoconvex CR manifold
Authors: Chang, D.-C.; Chang, S.-C.; Tie, J.; SHU-CHENG CHANG
Wed, 01 Jan 2014 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3848712014-01-01T00:00:00Z
- TOWARDS A plus B THEORY IN CONIFOLD TRANSITIONS FOR CALABI-YAU THREEFOLDShttps://scholars.lib.ntu.edu.tw/handle/123456789/405492Title: TOWARDS A plus B THEORY IN CONIFOLD TRANSITIONS FOR CALABI-YAU THREEFOLDS
Authors: Lee, Yuan-Pin; Lin, Hui-Wen; Wang, Chin-Lung; 林惠雯
Mon, 01 Jan 2018 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/4054922018-01-01T00:00:00Z
- Green Function, Painleve Vi Equation, and Eisenstein Series of Weight Onehttps://scholars.lib.ntu.edu.tw/handle/123456789/405504Title: Green Function, Painleve Vi Equation, and Eisenstein Series of Weight One
Authors: Chen, Zhijie; Kuo, Ting-Jung; Lin, Chang-Shou; Wang, Chin-Lung; 林長壽
Abstract: The behavior and the location of singular points of a solution to Painlevé VI equation could encode important geometric properties. For example, Hitchin's formula indicates that singular points of algebraic solutions are exactly the zeros of Eisenstein series of weight one. In this paper, we study the problem: How many singular points of a solution λ(t) to the Painlevé VI equation with parameter ( 1/8 , -1/8 , 1/8 , 3/8 ) might have in C\{0, 1}? Here t0 ∈ C\{0, 1} is called a singular point of λ(t) if λ(t0) ∈ {0, 1, t0,∞}. Based on Hitchin's formula, we explore the connection of this problem with Green function and the Eisenstein series of weight one. Among other things, we prove: (i) There are only three solutions which have no singular points in C\{0, 1}. (ii) For a special type of solutions (called real solutions here), any branch of a solution has at most two singular points (in particular, at most one pole) in C \ {0, 1}. (iii) Any Riccati solution has singular points in C\{0, 1}. (iv) For each N ≥ 5 and N = 6, we calculate the number of the real j-values of zeros of the Eisenstein series EN1 (τ ; k1, k2) of weight one, where (k1, k2) runs over [0,N - 1]2 with gcd(k1, k2,N) = 1. The geometry of the critical points of the Green function on a flat torus Eτ, as τ varies in the moduli M1, plays a fundamental role in our analysis of the Painlevé VI equation. In particular, the conjectures raised in [23] on the shape of the domain Ω5 ⊂ M1, which consists of tori whose Green function has extra pair of critical points, are completely solved here. © 2018 Project Euclid.
Mon, 01 Jan 2018 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/4055042018-01-01T00:00:00Z
- Mean Curvature Flows in Manifolds of Special Holonomyhttps://scholars.lib.ntu.edu.tw/handle/123456789/405513Title: Mean Curvature Flows in Manifolds of Special Holonomy
Authors: Tsai, Chung-Jun; Wang, Mu-Tao; 蔡忠潤
Mon, 01 Jan 2018 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/4055132018-01-01T00:00:00Z
- Motivic and quantum invariance under stratified mukai flopshttps://scholars.lib.ntu.edu.tw/handle/123456789/338025Title: Motivic and quantum invariance under stratified mukai flops
Authors: Fu, B.; Wang, C.-L.; CHIN-LUNG WANG
Tue, 01 Jan 2008 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3380252008-01-01T00:00:00Z
- On the topology of birational minimal modelshttps://scholars.lib.ntu.edu.tw/handle/123456789/338026Title: On the topology of birational minimal models
Authors: Wang, C.-L.; CHIN-LUNG WANG
Thu, 01 Jan 1998 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3380261998-01-01T00:00:00Z
- Estimates of the mean field equations with integer singular sources: Non-simple blowuphttps://scholars.lib.ntu.edu.tw/handle/123456789/398649Title: Estimates of the mean field equations with integer singular sources: Non-simple blowup
Authors: Kuo, T.-J.; Lin, C.-S.; CHANG-SHOU LIN
Fri, 01 Jan 2016 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3986492016-01-01T00:00:00Z
- Erratum: Calabi-yau theorem and hodge-laplacian heat equation in a closed strictly pseudoconvex cr (2n + 1)-manifold (Journal of Differential Geometry)https://scholars.lib.ntu.edu.tw/handle/123456789/398646Title: Erratum: Calabi-yau theorem and hodge-laplacian heat equation in a closed strictly pseudoconvex cr (2n + 1)-manifold (Journal of Differential Geometry)
Authors: Chang, D.-C.; Chang, S.-C.; Tie, J.; SHU-CHENG CHANG
Fri, 01 Jan 2016 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3986462016-01-01T00:00:00Z
- Prescribing scalar curvature on SN, Part 1: Apriori estimateshttps://scholars.lib.ntu.edu.tw/handle/123456789/292171Title: Prescribing scalar curvature on SN, Part 1: Apriori estimates
Authors: Chen, C.-C.; Lin, C.-S.; CHANG-SHOU LIN
Mon, 01 Jan 2001 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/2921712001-01-01T00:00:00Z
- Rigidity of proper holomorphic maps between symmetric domainshttps://scholars.lib.ntu.edu.tw/handle/123456789/304548Title: Rigidity of proper holomorphic maps between symmetric domains
Authors: Tsai, I.-H.; Tsai, I-Hsun
Fri, 01 Jan 1993 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3045481993-01-01T00:00:00Z
- Self-similar solutions and translating solitons for Lagrangian mean curvature flowhttps://scholars.lib.ntu.edu.tw/handle/123456789/355889Title: Self-similar solutions and translating solitons for Lagrangian mean curvature flow
Authors: Joyce, D.; Lee, Y.-I.; Tsui, M.-P.; YNG-ING LEE
Abstract: We construct many self-similar and translating solitons for Lagrangian mean curvature flow, including self-expanders and translating solitons with arbitrarily small oscillation on the Lagrangian angle. Our translating solitons play the same role as cigar solitons in Ricci flow, and are important in studying the regularity of Lagrangian mean curvature flow. Given two transverse Lagrangian planes ℝn in 핔n with sum of characteristic angles less than π, we show there exists a Lagrangian self-expander asymptotic to this pair of planes. The Maslov class of these self-expanders is zero. Thus they can serve as local models for surgeries on Lagrangian mean curvature flow. Families of self-shrinkers and self-expanders with different topologies are also constructed. This paper generalizes the work of Anciaux [1], Joyce [12], Lawlor [15], and Lee and Wang [18, 19]. © 2010 Journal of Differential Geometry.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3558892010-01-01T00:00:00Z
- The deformation of Lagrangian minimal surfaces in Kähler-Einstein surfaceshttps://scholars.lib.ntu.edu.tw/handle/123456789/337979Title: The deformation of Lagrangian minimal surfaces in Kähler-Einstein surfaces
Authors: Lee, Y.-I.; YNG-ING LEE
Thu, 01 Jan 1998 00:00:00 GMThttps://scholars.lib.ntu.edu.tw/handle/123456789/3379791998-01-01T00:00:00Z