Complete self-shrinkers confined into some regions of the space

DOI10.1007/s10455-013-9387-8zbMath1287.53007arXiv1212.4041OpenAlexW2041712050MaRDI QIDQ2436531

Stefano Pigola, Michele Rimoldi

Publication date: 25 February 2014

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.4041

zbMATH Keywords

weighted manifoldsdrifted Laplacianbounded self-shrinkershyperplane intersection

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons ⋮ Bi-Halfspace and Convex Hull Theorems for Translating Solitons ⋮ Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers ⋮ Parabolicity, Brownian exit time and properness of solitons of the direct and inverse mean curvature flow ⋮ The Frankel property for self-shrinkers from the viewpoint of elliptic PDEs ⋮ Smooth compactness of 𝑓-minimal hypersurfaces with bounded 𝑓-index ⋮ Rigidity and gap results for low index properly immersed self-shrinkers in \(\mathbb{R}^{m + 1}\) ⋮ Aspects of mean curvature flow solitons in warped products ⋮ Reilly's type inequality for the Laplacian associated to a density related with shrinkers for MCF ⋮ Parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights ⋮ Estimates for the first eigenvalue of \(\mathfrak{L}\)-operator on self-shrinkers ⋮ Halfspace type theorems for self-shrinkers ⋮ The rigidity and stability of complete 𝑓-minimal hypersurfaces in ℝⁿ×𝕊¹(𝕒) ⋮ Stability properties and topology at infinity of \(f\)-minimal hypersurfaces ⋮ Gradient estimates and Harnack inequalities for positive solutions of \(\mathfrak{L}u=\frac{\partial u}{\partial t}\) on self-shrinkers

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