Umbilicity and characterization of Pansu spheres in the Heisenberg group

Jih Hsin Cheng; Hung Lin Chiu; Jenn Fang Hwang; Paul Yang

doi:10.1515/crelle-2015-0044

Umbilicity and characterization of Pansu spheres in the Heisenberg group

Jih Hsin Cheng
, Hung Lin Chiu
, Jenn Fang Hwang
, Paul Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

For every n ≥ 2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group H_n. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p-mean (or horizontal-mean) curvature in H_n up to Heisenberg translations.

Original language	English (US)
Pages (from-to)	203-235
Number of pages	33
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2015
DOIs	https://doi.org/10.1515/crelle-2015-0044
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/crelle-2015-0044

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title = "Umbilicity and characterization of Pansu spheres in the Heisenberg group",

abstract = "For every n ≥ 2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group Hn. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p-mean (or horizontal-mean) curvature in Hn up to Heisenberg translations.",

author = "Cheng, \{Jih Hsin\} and Chiu, \{Hung Lin\} and Hwang, \{Jenn Fang\} and Paul Yang",

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year = "2015",

doi = "10.1515/crelle-2015-0044",

language = "English (US)",

volume = "2015",

pages = "203--235",

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T1 - Umbilicity and characterization of Pansu spheres in the Heisenberg group

AU - Cheng, Jih Hsin

AU - Chiu, Hung Lin

AU - Hwang, Jenn Fang

AU - Yang, Paul

PY - 2015

Y1 - 2015

N2 - For every n ≥ 2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group Hn. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p-mean (or horizontal-mean) curvature in Hn up to Heisenberg translations.

AB - For every n ≥ 2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group Hn. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p-mean (or horizontal-mean) curvature in Hn up to Heisenberg translations.

UR - https://www.scopus.com/pages/publications/84990203579

UR - https://www.scopus.com/pages/publications/84990203579#tab=citedBy

U2 - 10.1515/crelle-2015-0044

DO - 10.1515/crelle-2015-0044

M3 - Article

AN - SCOPUS:84990203579

SN - 0075-4102

VL - 2015

SP - 203

EP - 235

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

ER -

Umbilicity and characterization of Pansu spheres in the Heisenberg group

Abstract

All Science Journal Classification (ASJC) codes

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