naa a22 4500 510810551 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9288-7 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9288-7 Marquardt Thomas Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476, Potsdam-Golm, Germany aut Inverse Mean Curvature Flow for Star-Shaped Hypersurfaces Evolving in a Cone [Elektronische Daten] [Thomas Marquardt] For a given convex cone we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicular. The evolution of those hypersurfaces inside the cone yields a nonlinear parabolic Neumann problem. We show that one can use the convexity of the cone to prove long time existence of this flow. Finally, we show that the hypersurfaces converge smoothly to a piece of the round sphere. Mathematica Josephina, Inc., 2011 Inverse mean curvature flow nationallicence Nonlinear boundary value problem nationallicence Gradient estimate nationallicence Long time existence nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1303-1313 1050-6926 23:3<1303 2013 23 12220 https://doi.org/10.1007/s12220-011-9288-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9288-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Marquardt Thomas Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476, Potsdam-Golm, Germany aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1303-1313 1050-6926 23:3<1303 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer