TY - JOUR

T1 - Entropy bounds, compactness and finiteness theorems for embedded self-shrinkers with rotational symmetry

AU - Ma, John Man Shun

AU - Muhammad, Ali

AU - Møller, Niels Martin

N1 - Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston 2022 Independent Research Fund Denmark DFF Sapere Aude 7027-00110B Danish National Research Foundation CPH-GEOTOP-DNRF151 Carlsberg Foundation CF21-0680 The authors were partially supported by DFF Sapere Aude 7027-00110B, by CPH-GEOTOP-DNRF151 and by CF21-0680 from respectively the Independent Research Fund Denmark, the Danish National Research Foundation and the Carlsberg Foundation.

PY - 2022

Y1 - 2022

N2 - In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}}. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry.

AB - In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}}. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry.

U2 - 10.1515/crelle-2022-0073

DO - 10.1515/crelle-2022-0073

M3 - Journal article

AN - SCOPUS:85142388969

VL - 793

SP - 239

EP - 259

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

ER -