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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.

On strongly monotone flows

88%

Walter W.

Annales Polonici Mathematici

1997

tom 66

nr 1

269-274

M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Annales Polonici Mathematici

1 Ohta S.-i.

1 Walter W.

1 2014

1 1997

Wyniki wyszukiwania

On the Curvature and Heat Flow on Hamiltonian Systems

On strongly monotone flows