Volume 29, 2023
|Number of page(s)||24|
|Published online||19 June 2023|
C1,1-Rectifiability and Heintze–Karcher Inequality on Sn+1
School of Mathematical Sciences, Xiamen University, 361005, Xiamen, PR China
2 Institut für Mathematik, Goethe-Universität, 60325, Frankfurt, Germany
* Corresponding author: email@example.com
Accepted: 29 May 2023
In this paper, by isometrically embedding (Sn+1, gSn+1) into Rn+2, and using nonlinear analysis on the codimension-2 graphs, we will show that the level-sets of the distance function from the boundary of any open set in sphere, are C1,1-rectifiable. As a by-product, we establish a Heintze-Karcher-type inequality on sphere.
Mathematics Subject Classification: 35B65 / 49Q15 / 49Q20 / 53C21
Key words: Level-sets of distance function / C1,1-rectifiability / Heintze-Karcher-type inequality
© The authors. Published by EDP Sciences, SMAI 2023
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