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Stochastic differential inclusions of Langevin type on Riemannian manifolds

100%

Gliklikh Y., Obukhovskiĭ A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001

tom 21

nr 2

173-190

We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.

Plateau-Stein manifolds

100%

Gromov M.

Open Mathematics

2014

tom 12

nr 7

923-951

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles

88%

Bogdanovich S., Ermolitski A.

Open Mathematics

2004

tom 2

nr 5

615-623

Some results concerning almost hyperHermitian structures are considered, using the notions of the canonical connection and the second fundamental tensor field h of a structure on a Riemannian manifold which were introduced by the second author. With the help of any metric connection $$\tilde \nabla $$ on an almost Hermitian manifold M an almost hyperHermitian structure can be constructed in the defined way on the tangent bundle TM. A similar construction was considered in [6], [7]. This structure includes two basic anticommutative almost Hermitian structures for which the second fundamental tensor fields h 1 and h 2 are computed. It allows us to consider various classes of almost hyperHermitian structures on TM. In particular, there exists an infinite-dimensional set of almost hyperHermitian structures on TTM where M is any Riemannian manifold.

Ograniczanie wyników

2 Open Mathematics

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Bogdanovich S.

1 Ermolitski A.

1 Gliklikh Y.

1 Gromov M.

1 Obukhovskiĭ A.

1 2014

1 2004

1 2001

Wyniki wyszukiwania

Stochastic differential inclusions of Langevin type on Riemannian manifolds

Plateau-Stein manifolds

On almost hyperHermitian structures on Riemannian manifolds and tangent bundles