On decomposable Monge-Ampère equations.
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
In this paper, we prove by using the minimax principle that there exist infinitely many -equivariant harmonic maps from a specific Lorentz manifold to a compact Riemannian manifold.
We study finite -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then has isospectral non-isometric covers.