A Second Order Smooth Variational Principle on Riemannian Manifolds

ACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

Stochastic variational principle on riemannian manifolds

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Geodesic Connectedness of Semi-riemannian Manifolds

The problem of geodesic connectedness in semi-Riemannian manifolds (i.e. the question whether each two points of the manifold can be joined by a geodesic) has been widely studied from very different viewpoints. Our purpose is to review these semi-Riemannian techniques, and possible extensions. In the Riemannian case, it is natural to state this problem on (incomplete) manifolds with (possibly n...

Maximum principle for viscosity solutions on Riemannian manifolds

In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity version.