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On the Curvature and Heat Flow on Hamiltonian Systems

Shin-ichi Ohta — 2014

Analysis and Geometry in Metric Spaces

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 appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

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