Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

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

doi:10.1007/s00526-016-1006-7

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

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

Mathematics

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

5 Scopus citations

Abstract

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group H_n with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

Original language	English (US)
Article number	66
Journal	Calculus of Variations and Partial Differential Equations
Volume	55
Issue number	3
DOIs	https://doi.org/10.1007/s00526-016-1006-7
State	Published - Jun 1 2016

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

32V20
49Q10
53A10
Primary 35L80
Secondary 35J70

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10.1007/s00526-016-1006-7

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abstract = "We study immersed, connected, umbilic hypersurfaces in the Heisenberg group Hn with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.",

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AU - Cheng, Jih Hsin

AU - Chiu, Hung Lin

AU - Hwang, Jenn Fang

AU - Yang, Paul

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We study immersed, connected, umbilic hypersurfaces in the Heisenberg group Hn with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

AB - We study immersed, connected, umbilic hypersurfaces in the Heisenberg group Hn with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

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KW - 53A10

KW - Primary 35L80

KW - Secondary 35J70

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3

M1 - 66

ER -

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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