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Jet vanishing orders and effectivity of Kohn’s algorithm in dimension 3
Kim, Sung-Yeon,Zaitsev, Dmitri International Press of Boston, Inc. 2018 The Asian journal of mathematics Vol.22 No.3
<P>Our techniques here may be of broader interest for more general PDE systems, in the light of the recent program initiated by the breakthrough paper of Y.-T. Siu [S17].</P>
Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
Kwong, Kwok-Kun,Lee, Hojoo,Pyo, Juncheol International Press of Boston, Inc. 2018 Mathematical research letters Vol.25 No.2
<P>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-Nordstrom 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.</P>