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On the Curvature and Heat Flow on Hamiltonian Systems

100%

Ohta S.-i.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

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.

Sobolev-Kantorovich Inequalities

88%

Ledoux M.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

1 Ledoux M.

1 Ohta S.-i.

1 2015

1 2014

Wyniki wyszukiwania

On the Curvature and Heat Flow on Hamiltonian Systems

Sobolev-Kantorovich Inequalities