Existenz und Nicht-Existenz monotoner Größen für geometrische Flüsse : Potenzen von mittlerer und Gaußscher Krümmung

Abstract

We explore geometric flow equations. Our main results concern flows by powers of the mean curvature and Gauss curvature. Firstly we prove longtime existence for entire graphs under mild assumptions. Secondly for closed hypersurfaces we show the existence and the non-existence of certain monotone quantities that ensure convergence to round points or convergence to spheres at infinity. Thirdly we prove that pinched hypersurfaces shrink to round points using a computer algebra system.