Abstract
We use the weighted Hsiung-Minkowski integral formulas and Brendle’s inequality to show new rigidity results. We prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild and Reissner-Nordström spaces, where the Alexandrov reflection principle is not available. We also prove that, in Euclidean space, the only closed immersed self-expanding solitons to the weighted generalized inverse curvature flow of codimension one are round hyperspheres.
| Original language | English |
|---|---|
| Pages (from-to) | 597-616 |
| Number of pages | 20 |
| Journal | Mathematical Research Letters |
| Volume | 25 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2018 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces. / Kwok-Kun, Kwong; Lee, Hojoo; Pyo, Juncheol.
In: Mathematical Research Letters, Vol. 25, No. 2, 01.01.2018, p. 597-616.Research output: Contribution to journal › Article
TY - JOUR
T1 - Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
AU - Kwok-Kun, Kwong
AU - Lee, Hojoo
AU - Pyo, Juncheol
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We use the weighted Hsiung-Minkowski integral formulas and Brendle’s inequality to show new rigidity results. We prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild and Reissner-Nordström spaces, where the Alexandrov reflection principle is not available. We also prove that, in Euclidean space, the only closed immersed self-expanding solitons to the weighted generalized inverse curvature flow of codimension one are round hyperspheres.
AB - We use the weighted Hsiung-Minkowski integral formulas and Brendle’s inequality to show new rigidity results. We prove Alexandrov type results for closed embedded hypersurfaces with radially symmetric higher order mean curvature in a large class of Riemannian warped product manifolds, including the Schwarzschild and Reissner-Nordström spaces, where the Alexandrov reflection principle is not available. We also prove that, in Euclidean space, the only closed immersed self-expanding solitons to the weighted generalized inverse curvature flow of codimension one are round hyperspheres.
UR - http://www.scopus.com/inward/record.url?scp=85049912754&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85049912754&partnerID=8YFLogxK
U2 - 10.4310/MRL.2018.v25.n2.a13
DO - 10.4310/MRL.2018.v25.n2.a13
M3 - Article
AN - SCOPUS:85049912754
VL - 25
SP - 597
EP - 616
JO - Mathematical Research Letters
JF - Mathematical Research Letters
SN - 1073-2780
IS - 2
ER -