We study compact Riemannian manifolds .M;g/ for which the light from any given point x 2 M can be shaded away from any other point y 2 M by finitely many point shades in M . Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat metrics. Using entropy consider...

In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that “generic” finitely generated groups have no smooth volume preserving actions on compact manifolds.

We classify compact anti-self-dual Hermitian surfaces and compact four-dimensional conformally flat manifolds for which the group of orientation preserving conformal transformations contains a two-dimensional toms. As a corollary, we derive a topological classification of compact self-dual manifolds for which the group of conformal transformations contains a two-dimensional toms. Mathematics Su...

In this article we study the limiting behavior of the KählerRicci flow on complete non-compact Kähler manifolds. We provide sufficient conditions under which a complete non-compact gradient KählerRicci soliton is biholomorphic to C. We also discuss the uniformization conjecture by Yau [15] for complete non-compact Kähler manifolds with positive holomorphic bisectional curvature.

In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the bo...