Complete \(\lambda\)-hypersurfaces in Euclidean spaces

DOI10.1007/s11401-022-0365-yzbMath1505.53010OpenAlexW4313183360MaRDI QIDQ2095595

Guoxin Wei, Qing-Ming Cheng

Publication date: 17 November 2022

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-022-0365-y

zbMATH Keywords

mean curvature flowrigidity theoremself-shrinkerweighted volume\( \lambda \)-hypersurface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Rigidity results (53C24) Flows related to mean curvature (53E10)

Related Items

An immersed \(S^n \lambda\)-hypersurface

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Embedded self-similar shrinkers of genus 0
• 2-dimensional complete self-shrinkers in \(\mathbb R^3\)
• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
• \(\mathcal{F}\)-stability for self-shrinking solutions to mean curvature flow
• Rigidity theorems of \(\lambda\)-hypersurfaces
• Construction of complete embedded self-similar surfaces under mean curvature flow. III
• The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
• Flow by mean curvature of convex surfaces into spheres
• Examples of compact \(\lambda\)-hypersurfaces in Euclidean spaces
• Asymptotic behavior for singularities of the mean curvature flow
• Mean curvature evolution of entire graphs
• Construction of complete embedded self-similar surfaces under mean curvature flow. II
• The normalized curve shortening flow and homothetic solutions
• The Brunn-Minkowski inequality in Gauss space
• A density function and the structure of singularities of the mean curvature flow
• Mean curvature self-shrinkers of high genus: non-compact examples
• Complete bounded \(\lambda\)-hypersurfaces in the weighted volume-preserving mean curvature flow
• Rigidity and curvature estimates for graphical self-shrinkers
• A survey of closed self-shrinkers with symmetry
• Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• Complete \(\lambda\)-surfaces in \(\mathbb{R}^3\)
• Complete self-shrinkers of the mean curvature flow
• Volume estimates and classification theorem for constant weighted mean curvature hypersurfaces
• Rigidity theorems for complete \(\lambda\)-hypersurfaces
• The structure of Gaussian minimal bubbles
• Complete self-shrinkers with constant norm of the second fundamental form
• A new pinching theorem for complete self-shrinkers and its generalization
• \(\lambda\)-Hypersurfaces on shrinking gradient Ricci solitons
• On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface
• Rigidity of generic singularities of mean curvature flow
• Gap theorems for complete \(\lambda\)-hypersurfaces
• 1-dimensional solutions of the \(\lambda \)-self shrinkers
• A Bernstein type theorem for self-similar shrinkers
• Local rigidity theorems for minimal hypersurfaces
• Self-similar solutions to the curve shortening flow
• Gap and rigidity theorems of 𝜆-hypersurfaces
• Lower volume growth estimates for self-shrinkers of mean curvature flow
• Self-shrinkers with a rotational symmetry
• The rigidity theorems of self-shrinkers
• Construction of complete embedded self-similar surfaces under mean curvature flow. Part I.
• The volume preserving mean curvature flow.
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Computation of Self-Similar Solutions for Mean Curvature Flow
• On the Rigidity of Mean Convex Self-Shrinkers
• A rigidity theorem on the second fundamental form for self-shrinkers
• Volume estimate about shrinkers
• Convexity of 𝜆-hypersurfaces
• The second pinching theorem for complete $\boldsymbol{\lambda}$-hypersurfaces
• Geometry of complete $\boldsymbol{\lambda}$-hypersurfaces
• A note on rigidity theorem of λ-hypersurfaces
• A gap theorem of self-shrinkers
• Immersed self-shrinkers
• Umbilical Points and W-Surfaces
• Symmetric convex sets with minimal Gaussian surface area