The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
From MaRDI portal
Publication:744919
DOI10.1007/s10711-015-0057-9zbMath1325.53079arXiv1307.7088OpenAlexW2007761567MaRDI QIDQ744919
Publication date: 12 October 2015
Published in: Geometriae Dedicata (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1307.7088
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)
Related Items
Ruled surfaces of generalized self-similar solutions of the mean curvature flow ⋮ Gap and rigidity theorems of 𝜆-hypersurfaces ⋮ Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons ⋮ Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons ⋮ Compactness and Rigidity of λ-Surfaces ⋮ Complete bounded \(\lambda\)-hypersurfaces in the weighted volume-preserving mean curvature flow ⋮ A Bernstein type theorem for entire graphic 2-dimensional \(\Lambda \)-submanifolds in \(\mathbf{R}^4 \) ⋮ Gap theorems for complete \(\lambda\)-hypersurfaces ⋮ 1-dimensional solutions of the \(\lambda \)-self shrinkers ⋮ Spacelike hypersurfaces immersed in weighted standard static spacetimes: uniqueness, nonexistence and stability ⋮ Complete space-like \(\lambda \)-surfaces in the Minkowski space \(\mathbb{R}_1^3\) with the second fundamental form of constant length ⋮ Weighted Minkowski’s existence theorem and projection bodies ⋮ Stable capillary hypersurfaces and the partitioning problem in balls with radial weights ⋮ An immersed \(S^n \lambda\)-hypersurface ⋮ A new pinching theorem for complete self-shrinkers and its generalization ⋮ Examples of compact embedded convex \(\lambda \)-hypersurfaces ⋮ \(\lambda\)-Hypersurfaces on shrinking gradient Ricci solitons ⋮ Some rigidity properties for \(\lambda\)-self-expanders ⋮ Stable and isoperimetric regions in some weighted manifolds with boundary ⋮ Isoperimetric and stable sets for log-concave perturbations of Gaussian measures ⋮ A note on mean convex 𝜆-surfaces in ℝ³ ⋮ Three candidate plurality is stablest for small correlations ⋮ Essential spectrum of the weighted Laplacian on noncompact manifolds and applications ⋮ \(f\)-stability of spacelike hypersurfaces in weighted spacetimes ⋮ A Bernstein-type theorem for -submanifolds with flat normal bundle in the Euclidean spaces ⋮ Rigidity theorems for complete \(\lambda\)-hypersurfaces ⋮ Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces ⋮ The structure of Gaussian minimal bubbles ⋮ On the existence of a closed, embedded, rotational \(\lambda \)-hypersurface ⋮ Hopf-type theorem for self-shrinkers ⋮ Variational characterizations of \(\xi\)-submanifolds in the Eulicdean space \(\mathbb{R}^{m+p}\) ⋮ The Gaussian double-bubble and multi-bubble conjectures ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces ⋮ Convexity of 𝜆-hypersurfaces
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generic mean curvature flow. I: Generic singularities
- Spherical harmonics and approximations on the unit sphere. An introduction
- Construction of complete embedded self-similar surfaces under mean curvature flow. III
- Stability properties and topology at infinity of \(f\)-minimal hypersurfaces
- A note on the stability theorem of J. L. Barbosa and M. do Carmo for closed surfaces of constant mean curvature
- Stability of hypersurfaces with constant mean curvature
- The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
- The Brunn-Minkowski inequality in Gauss space
- Curvature estimates for minimal hypersurfaces
- Mean curvature self-shrinkers of high genus: non-compact examples
- Isoperimetric regions in cones
- Stability of the Wulff shape
- Stability and compactness for complete 𝑓-minimal surfaces
This page was built for publication: The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
