On the curvature and heat flow on Hamiltonian systems

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--Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

45 pages; Minor modifications everywhere, added Example 7.4, expanded Example 8.8; To appear in Anal. Geom. Metr. Spaces

References in corpus (2)

• On Interpolation and Curvature via Wasserstein Geodesics
• Local gradient estimate for harmonic functions on Finsler manifolds

Cited by in corpus (1)

• $(K,N)$-convexity and the curvature-dimension condition for negative $N$