Contraction semigroups and representations.
We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.
The space of Kähler metrics in a fixed Kähler class on a projective Kähler manifold is an infinite dimensional symmetric space whose geodesics are solutions of a homogeneous complex Monge-Ampère equation in , where is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials of may be approximated in a weak sense by geodesics of the finite dimensional symmetric space of Bergman metrics of height . In this article we prove that in in the case of...
We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.