Abstract
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.
Original language | English |
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Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 793 |
Pages (from-to) | 239-259 |
ISSN | 0075-4102 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
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.