TY - JOUR
T1 - Brendle’s Inequality on Static Manifolds
AU - Wang, Xiaodong
AU - Wang, Ye Kai
N1 - Funding Information:
Acknowledgements The first author is partially supported by Simons Foundation Collaboration Grant for Mathematicians #312820. The second author would like to thank Professor Mu-Tao Wang for his constant encouragement, Po-Ning Chen and Pei-Ken Hung for helpful discussions. We would also like to thank Professor Luen-Fai Tam for his comments on the paper.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We generalize Brendle’s geometric inequality considered in Brendle (Publ Math Inst Hautes Études Sci 117:247–269, 2013) to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperbolic manifolds in the spirit of Chruściel and Simon (J Math Phys 42(4):1779–1817, 2001).
AB - We generalize Brendle’s geometric inequality considered in Brendle (Publ Math Inst Hautes Études Sci 117:247–269, 2013) to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a consequence, we obtain a reverse Penrose inequality on static asymptotically locally hyperbolic manifolds in the spirit of Chruściel and Simon (J Math Phys 42(4):1779–1817, 2001).
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U2 - 10.1007/s12220-017-9814-3
DO - 10.1007/s12220-017-9814-3
M3 - Article
AN - SCOPUS:85014576605
VL - 28
SP - 152
EP - 169
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 1
ER -