On the existence of nontrivial extremal metrics on complete noncompact surfaces
Journal
Mathematische Annalen
Journal Volume
324
Journal Issue
3
Pages
465-490
Date Issued
2002
Author(s)
Abstract
In this paper, we consider the 2-dimensional local Calabi flow on a complete noncompact surface (∑, g0). Then, based on the Harnack-type estimate, we show the long-time existence and asymptotic convergence of a subsequence of solutions of such a flow on (∑, g0) with R0 ≤ 0 and R0 bounded from above by a negative constant on a ball. For its applications, this will lead to the existence of extremal metrics on a complete noncompact surface of finite topological type. In particular, there exists an extremal metric of nonconstant Gaussian curvature on ∑ = H2 or R2.
SDGs
Type
journal article