<i>B</i> ‐sub‐manifolds and their stability

Ма, Ли

doi:10.1002/mana.200310439

Mathematische Nachrichten

2006

DOI: 10.1002/mana.200310439

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B ‐sub‐manifolds and their stability

Ли Ма

Abstract: In this paper, we show that the "grim reaper" in the curve-shortening problem is stable in the sense of "symmetric stable" defined by K. Smoczyk. We also briefly discuss the graphic B-minimal sub-manifold in R n+k .

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Cited by 7 publications

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Conformal solitons to the mean curvature flow and minimal submanifolds

Arezzo

Sun

2012

Mathematische Nachrichten

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In this note we prove a correspondence, first found by Smoczyk in the hypersurface case, between conformal solitons to the mean curvature flow in an ambient manifold N and minimal submanifolds in a different space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$N\times \textbf {R}$\end{document}. This naturally leads to a new natural stability notion for conformal solitons. We show that this corresponds to the recent Colding‐Minicozzi's F‐stability for codimension one self‐shrinkers in euclidean space. In this spirit we can give some classification results for stable conformal solitons, answering two questions of Smoczyk.

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Conformal solitons to the mean curvature flow and minimal submanifolds

Arezzo

Sun

2012

Mathematische Nachrichten

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Stability Property and Dirichlet Problem for Translating Solitons

Ma¹

2021

Results Math

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Bernstein theorem for translating solitons of hypersurfaces

2019

manuscripta math.

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In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in R n+1 , giving some conditions under which a translating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in R n+k , namely, if the L n norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.Mathematics Subject Classification 2010: 53C21,53C44

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B ‐sub‐manifolds and their stability

Abstract: In this paper, we show that the "grim reaper" in the curve-shortening problem is stable in the sense of "symmetric stable" defined by K. Smoczyk. We also briefly discuss the graphic B-minimal sub-manifold in R n+k .

Cited by 7 publications

References 8 publications

Conformal solitons to the mean curvature flow and minimal submanifolds

Conformal solitons to the mean curvature flow and minimal submanifolds

Stability Property and Dirichlet Problem for Translating Solitons

Bernstein theorem for translating solitons of hypersurfaces

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