On the curvature and heat flow on Hamiltonian systems
Differential Geometry
2014-11-07 v2 Analysis of PDEs
Abstract
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation. We prove the appropriate generalizations of Bochner--Weitzenb\"ock formula and Laplacian comparison theorem, and study the heat flow.
Keywords
Cite
@article{arxiv.1308.5746,
title = {On the curvature and heat flow on Hamiltonian systems},
author = {Shin-ichi Ohta},
journal= {arXiv preprint arXiv:1308.5746},
year = {2014}
}
Comments
45 pages; Minor modifications everywhere, added Example 7.4, expanded Example 8.8; To appear in Anal. Geom. Metr. Spaces