The entropy formulas for the CR heat equation and their applications on pseudohermitian (2n + 1)-manifolds
Journal
Pacific Journal of Mathematics
Journal Volume
246
Journal Issue
1
Pages
1-29
Date Issued
2010
Author(s)
Wu, C.-T.
Abstract
We derive Perelman's and Nash-type entropy formulas for the CR heat equation on closed pseudohermitian (2n + 1)-manifolds and show that it is monotone nonincreasing if its pseudohermitian Ricci curvature minus (n + 1)/2 times the pseudohermitian torsion is nonnegative.As results, we are able to obtain an integral version of the subgradient estimate for the CR heat equation and an upper bound estimate for the first positive eigenvalue of the sublaplacian by using the CR Bochner formulas and CR Harnacktype inequality.As a byproduct, we obtain a sharp lower bound estimate for the first positive eigenvalue of the sublaplacian on a closed pseudohermitian (2n + 1)-manifold.
SDGs
Type
journal article