Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces
2021 ◽
Vol 0
(0)
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Keyword(s):
Abstract We prove that, for every closed (not necessarily convex) hypersurface Σ in ℝ n + 1 {\mathbb{R}^{n+1}} and every p > n {p>n} , the L p {L^{p}} -norm of the trace-free part of the anisotropic second fundamental form controls from above the W 2 , p {W^{2,p}} -closeness of Σ to the Wulff shape. In the isotropic setting, we provide a simpler proof. This result is sharp since in the subcritical regime p ≤ n {p\leq n} , the lack of convexity assumptions may lead in general to bubbling phenomena. Moreover, we obtain a stability theorem for quasi-Einstein (not necessarily convex) hypersurfaces and we improve the quantitative estimates in the convex setting.
2000 ◽
Vol 24
(1)
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pp. 43-48
2009 ◽
Vol 356
(1)
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pp. 237-241
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Keyword(s):
2009 ◽
Vol 109A
(2)
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pp. 187-200
Keyword(s):
1994 ◽
Vol 2
(1)
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pp. 167-172
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2016 ◽
Vol 39
(1)
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pp. 173-185
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2019 ◽
Vol 16
(03)
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pp. 401-442