A maximum principle for evolution Hamilton–Jacobi equations on Riemannian manifolds

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.

A Maximum Principle for Positive Elliptic Pseudo-differential Operators on Closed Riemannian Manifolds

In this note we establish the positivity of Green’s functions for a class of elliptic differential operators on closed, Riemannian manifolds

Sufficient Decrease Principle on Riemannian Manifolds

Tools from Riemannian geometry (suitable Riemannian metric, exponential map, search along geodesics, covariant differentiation, sectional curvature, etc) are now used in Mathematical Programming to obtain deeply theoretical results and practical algorithms [3]-[11]. §1 lists basic propositions appearing in the numerical finding of a critical point of a real function defined on a Riemannian mani...

Stochastic variational principle on riemannian manifolds

Monge-Ampère Equations on Riemannian Manifolds

where gij denotes the metric of M , g = det(gij) > 0 and φ ∈ C∞(∂Ω), ψ > 0 is C∞ with respect to (x, z, p) ∈ Ω̄× R× TxM , TxM denotes the tangent space at x ∈M . Monge-Ampère equations arise naturally from some problems in differential geometry. The Dirichlet problem in Euclidean space R has been widely investigated. In this case the solvability has been reduced to the existence of strictly conv...