The p-widths of a surface

DOI10.1007/s10240-023-00141-7arXiv2107.11684MaRDI QIDQ6161725

Otis Chodosh, Christos Mantoulidis

Publication date: 5 June 2023

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.11684

zbMATH Keywords

minimal submanifoldsLusternik-Schnirelmann categorygeodesic netsp-widthsmin-max-sequencesWeyl laws

Mathematics Subject Classification ID

Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (2)

On the equidistribution of closed geodesics and geodesic nets ⋮ The first width of non-negatively curved surfaces with convex boundary

Cites Work

• Finite Morse Index Implies Finite Ends
• An Infinite Dimensional Version of Sard's Theorem
• The elliptic sine-Gordon equation in a half plane
• Geodesic Nets: Some Examples and Open Problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Families of short cycles on Riemannian surfaces
• On variational characterization of four-end solutions of the Allen-Cahn equation in the plane
• The existence of embedded minimal hypersurfaces
• Embedded minimal tori in \(S^3\) and the Lawson conjecture
• Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions
• End-to-end construction for the Allen-Cahn equation in the plane
• Morse index and multiplicity of \(\min\text{-}\max\) minimal hypersurfaces
• Min-max hypersurface in manifold of positive Ricci curvature
• Interface foliation near minimal submanifolds in Riemannian manifolds with positive Ricci curvature
• A viscosity method in the min-max theory of minimal surfaces
• The space of 4-ended solutions to the Allen-Cahn equation in the plane
• On stable critical points for a singular perturbation problem
• Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane
• Minimax problems related to cup powers and Steenrod squares
• The length of a shortest geodesic net on a closed Riemannian manifold
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• The Toda system and clustering interfaces in the Allen-Cahn equation
• Width and mean curvature flow
• Spectral analysis of the elliptic sine-Gordon equation in the quarter plane
• Singularities, expanders and topology of maps. I: Homology versus volume in the spaces of cycles
• Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
• A nonparametric proof of the theorem of Lusternik and Schnirelman
• On the equivalence of the first and second order equations for gauge theories
• Simple closed geodesics on convex surfaces
• Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
• The structure of stationary one dimensional varifolds with positive density
• Shortening embedded curves
• Isoperimetry of waists and concentration of maps
• The Allen-Cahn equation on closed manifolds
• Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in \({\mathbb R}^2\)
• Min-max for phase transitions and the existence of embedded minimal hypersurfaces
• Weyl law for the volume spectrum
• Density of minimal hypersurfaces for generic metrics
• Volume, diameter and the minimal mass of a stationary 1-cycle
• Towards classification of multiple-end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\)
• Boundary value problems for the elliptic sine-Gordon equation in a semi-strip
• Bound states of the elliptic sine-Gordon equation
• Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
• Existence of hypersurfaces with prescribed mean curvature I -- generic min-max
• The index and nullity of the Lawson surfaces \(\xi_{g,1}\)
• The catenoid estimate and its geometric applications
• A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory
• Ground states of semilinear elliptic problems with applications to the Allen-Cahn equation on the sphere
• Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen-Cahn
• On the multiplicity one conjecture in min-max theory
• A proof of the multiplicity 1 conjecture for min-max minimal surfaces in arbitrary codimension
• Allen-Cahn min-max on surfaces
• Morse index of multiplicity one min-max minimal hypersurfaces
• Generic scarring for minimal hypersurfaces along stable hypersurfaces
• Minimal 2-spheres in 3-spheres
• Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
• Min-max theory for networks of constant geodesic curvature
• The second inner variation of energy and the Morse index of limit interfaces
• Genus bounds for min-max minimal surfaces
• The width of ellipsoids
• Min-max theory for constant mean curvature hypersurfaces
• Second order estimate on transition layers
• Min-max minimal hypersurface in \((M^{n+1}, g)\) with \(\mathrm{Ric} > 0\) and \(2 \leq n \leq 6\)
• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
• Minimal hypersurfaces with bounded index
• Equidistribution of minimal hypersurfaces for generic metrics
• The classification of four-end solutions to the Allen-Cahn equation on the plane
• Min-max theory and the Willmore conjecture
• A general regularity theory for stable codimension 1 integral varifolds
• Shapes of geodesic nets
• Complete minimal surfaces in \(S^ 3\)
• The homotopy groups of the integral cycle groups
• Minimal submanifolds from the abelian Higgs model
• Existence of infinitely many minimal hypersurfaces in closed manifolds
• A Viscosity method for the min-max construction of closed geodesics
• The Dirichlet-to-Neumann map for the elliptic sine-Gordon equation
• Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
• Minimal Networks: A Review
• Lower Semi-continuity of the Index in the Viscosity Method for Minimal Surfaces
• Genus bounds for minimal surfaces arising from min-max constructions
• Geodesic nets on the 2-sphere
• Regularity of stable minimal hypersurfaces
• On the partition of the 2-sphere by geodesic nets
• Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces
• Doubling and Desingularization Constructions for Minimal Surfaces
• Moduli space theory for the Allen-Cahn equation in the plane
• Minimal surfaces in $$S^3$$ : a survey of recent results
• The (p;m)-width of Riemannian manifolds and its realization
• Existence of curves with constant geodesic curvature in a Riemannian 2-sphere
• The Regularity of Parametrized Integer Stationary Varifolds in Two Dimensions
• ON THE EXISTENCE OF CLOSED GEODESICS ON TWO-SPHERES
• On the bumpy metrics theorem for minimal submanifolds

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