A rigidity theorem for codimension one shrinking gradient Ricci solitons in \(\mathbb R^{n+1}\)

DOI10.1007/S00526-015-0929-8zbMath1335.53060arXiv1410.5856OpenAlexW1846795075MaRDI QIDQ5963598

Peng Lu, Yi Yan Xu, Pengfei Guan

Publication date: 22 February 2016

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5856

zbMATH Keywords

splitting theoremnonnegative curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24)

Related Items (5)

Shrinkers with curvature-pinching conditions are compact ⋮ Higher dimensional steady Ricci solitons with linear curvature decay ⋮ Curvature estimates for immersed hypersurfaces in Riemannian manifolds ⋮ Classification of gradient steady Ricci solitons with linear curvature decay ⋮ Interior \(C^2\) regularity of convex solutions to prescribing scalar curvature equations

Cites Work

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• Hypersurfaces of prescribed curvature measure
• On shrinking gradient Ricci solitons with nonnegative sectional curvature
• On the classification of gradient Ricci solitons
• On complete gradient shrinking Ricci solitons
• A compactness theorem for complete Ricci shrinkers
• Ancient solutions to Kähler-Ricci flow
• Strong uniqueness of the Ricci flow
• On a classification of gradient shrinking solitons
• Convexity of solutions of semilinear elliptic equations
• Four-manifolds with positive curvature operator
• Hypersurfaces with constant scalar curvature
• Ricci flow and nonnegativity of sectional curvature
• Three-manifolds with positive Ricci curvature
• The spherical images of convex hypersurfaces
• Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons
• On gradient Ricci solitons
• Gradient shrinking solitons with vanishing Weyl tensor
• Manifolds with positive curvature operators are space forms
• A microscopic convexity principle for nonlinear partial differential equations
• ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS
• Noncompact shrinking four solitons with nonnegative curvature
• Global C²‐Estimates for Convex Solutions of Curvature Equations

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