Index estimate of self-shrinkers in $\mathbb {R}^3$ with asymptotically conical ends

DOI10.1090/proc/14306zbMath1501.53005arXiv1803.09852OpenAlexW2964177183MaRDI QIDQ4644464

Nicolau Sarquis Aiex

Publication date: 7 January 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09852

zbMATH Keywords

Morse indexself-shrinkersGaussian harmonic formsweighted \( L^2\)-norm

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Flows related to mean curvature (53E10)

Related Items (3)

Bounds on the index of rotationally symmetric self-shrinking tori ⋮ Numerically computing the index of mean curvature flow self-shrinkers ⋮ Index and first Betti number of \(f\)-minimal hypersurfaces and self-shrinkers

Cites Work

• Volume growth eigenvalue and compactness for self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• On the finiteness of the Morse index for Schrödinger operators
• On the topology and index of minimal surfaces
• Stability properties and topology at infinity of \(f\)-minimal hypersurfaces
• Asymptotic behavior for singularities of the mean curvature flow
• On complete minimal surfaces with finite Morse index in three manifolds
• Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\)
• One-sided complete stable minimal surfaces
• Index bounds for minimal hypersurfaces of the sphere
• Uniqueness of self-similar shrinkers with asymptotically conical ends
• Interior estimates for elliptic systems of partial differential equations
• The heat kernel weighted Hodge Laplacian on noncompact manifolds
• Gaussian Harmonic Forms and two-dimensional self-shrinking surfaces

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