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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.
Let $(M,g)$ be a complete three dimensional Riemannian manifold with boundary $partial M$. Given smooth functions $K(x)>0$ and $c(x)$ defined on $M$ and $partial M$, respectively, it is natural to ask whether there exist metrics conformal to $g$ so t
Given a Riemannian spin^c manifold whose boundary is endowed with a Riemannian flow, we show that any solution of the basic Dirac equation satisfies an integral inequality depending on geometric quantities, such as the mean curvature and the ONeill t
This paper provides a characterization of functions of bounded variation (BV) in a compact Riemannian manifold in terms of the short time behavior of the heat semigroup. In particular, the main result proves that the total variation of a function equ
In this article we study a class of prescribed curvature problems on complete noncompact Riemannian manifolds. To be precise, we derive local $C^0$-estimate under an asymptotic condition which is in effect optimal, and prove the existence of complete
We obtain a dynamical--topological obstruction for the existence of isometric embedding of a Riemannian manifold-with-boundary $(M,g)$: if the first real homology of $M$ is nontrivial, if the centre of the fundamental group is trivial, and if $M$ is