We consider mean-convex Alexandrov embedded surfaces in the round unit 3-sphere, and show under which conditions it is possible to continuously deform these preserving mean-convex Alexandrov embeddedness.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Alexandrov embedding”
We prove the existence of two Alexandrov embedded closed magnetic geodesics on any two dimensional sphere with nonnegative Gauss curvature.
We introduce the moduli space of spectral curves of constant mean curvature (\cmc\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techni…
Embeds finite Alexandrov spaces into Euclidean products.
problem Embedding Alexandrov spaces into Euclidean products.
method Canonical embedding into a product of Alexandrov and Euclidean spaces.
result Affine functions on X arise from Euclidean functions.
Non-positively curved surfaces can be embedded in flat spacetime.
problem Embedding surfaces with non-positive curvature in flat spacetime.
method Polyhedral approximation to prove isometric embedding.
result Metric of non-positive curvature can be embedded as a convex spacelike Cauchy surface.
Constructs special surfaces in hyperbolic space with constant mean curvature.
problem Creating surfaces with specific geometric properties in hyperbolic space.
method Using the DPW method to construct surfaces with constant mean curvature.
result Constructs surfaces with constant mean curvature in hyperbolic space.
New -hypersurfaces not isometric to standard spheres.
problem No Alexandrov theorem for -hypersurfaces.
method Constructing compact embedded -hypersurfaces diffeomorphic to a sphere.
result Found -hypersurfaces not isometric to standard spheres.
Alexandrov immersed surfaces maintain their properties under mean curvature flow.
problem Preserving Alexandrov immersivity in mean curvature flow.
method Mean curvature flow techniques adapted for Alexandrov immersed, 2D surfaces.
result Mean curvature flow properties hold for Alexandrov immersed surfaces.
Paper proves spheres are unique in warped spaces.
problem Proving constant mean curvature spheres are unique in warped product manifolds.
method Generalizes proofs by Reilly, Ros, and Brendle.
result Proves rigidity result for constant mean curvature hypersurfaces in warped product manifolds.
Paper proves Allard's theorem in Alexandrov spaces.
problem Proving Allard's theorem in non-collapsed Alexandrov spaces.
method Developed an intrinsic proof for Riemannian manifolds, then extended to Alexandrov spaces using approximation theorem.
result Explicit constants for constants in terms of geometric data.
Proves new inequality for hyperbolic space hypersurfaces.
problem Finding inequalities for hypersurfaces in hyperbolic space.
method Proves a Heintze-Karcher type inequality for shifted mean convex hypersurfaces.
result Proves Alexandrov type theorem and uniqueness result for hypersurfaces.
New method characterizes minimal surfaces in 3D space.
problem Characterizing minimal surfaces in 3D space.
method Alexandrov Reflection Method
result Embedded minimal free boundary annuli in are the critical catenoid.
New rigidity results for hypersurfaces in warped product manifolds and Euclidean space.
problem Rigidity of hypersurfaces in warped product manifolds and Euclidean space.
method Weighted Hsiung-Minkowski integral formulas and Brendle's inequality.
result New rigidity results for hypersurfaces in specific manifolds.
We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.
This is a continuation of the joint paper with the same title by A.Belenkiy and Yu.Burago. It is proved here that two homeomorphic closed Alexandrov surfaces (of bounded integral curvature) are bi-Lipschitz with a constant depending only on upper bounds of their Euler number, diameters, negative integral curvatures, an…
Study of minimal annuli in hyperbolic space with horizontal ends, showing constraints on boundary curves.
problem Constraints on boundary curves of properly embedded minimal annuli in .
method Analysis of moduli space of properly Alexandrov-embedded, minimal annuli with horizontal ends.
result Boundary curves of minimal annuli are not fully prescribable, but the bottom curve and neck position are fixed, with top curve up to translation and tilt.
We show that one-sided Alexandrov embedded constant mean curvature cylinders of finite type in the 3-sphere are surfaces of revolution. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3-sphere are rotational.
The study constructs minimal surfaces in a product space with specific properties.
problem Constructing minimal surfaces with specific topological and geometric properties in a product space.
method 1-parameter families of complete properly Alexandrov-embedded minimal surfaces with dihedral symmetry and finite total curvature.
result Examples of minimal surfaces with genus 1 and 2k ends in quotient spaces.
We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the minimal, the embedded, and the Alexandrov embedded tori therein. We conclude with an instability result.
In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC surfaces with two ends and finite genus. Here, we construct the complete family of embedded CMC surfaces with three ends and genus zero; the…
In this paper, we are concerned with hypersurfaces in with constant r-mean curvature, to be called -hypersurfaces. We construct examples of complete -hypersurfaces which are invariant by parabolic screw motion or by rotation. We prove that there is a unique rotational strictly convex entire $H_r…
The paper proves rigidity results for capillary hypersurfaces in hyperbolic space.
problem Understanding the rigidity of capillary hypersurfaces in hyperbolic space.
method Proving a Heintze-Karcher type inequality and applying it to Alexandrov type theorems.
result Rigidity results for capillary hypersurfaces, including totally umbilical and totally geodesic cases.
Paper extends Wente's result to anisotropic capillary surfaces in half-spaces.
problem Extending Wente's result to anisotropic capillary surfaces.
method New Heintze-Karcher inequality and Minkowski formula.
result Anisotropic capillary hypersurfaces in half-spaces are Wulff shapes.
Logarithmic Sobolev inequality proven for non-compact self-shrinkers.
problem Establishing a logarithmic Sobolev inequality for non-compact self-shrinkers.
method Using Alexandrov-Bakelman-Pucci (ABP) method to prove the inequality for Euclidean space, then applying this method to non-compact self-shrinkers.
result Optimal logarithmic Sobolev inequality for complete, non-compact, properly embedded self-shrinkers.
New method proves Alexandrov theorem for curved spacetimes.
problem Proving Alexandrov theorem for curved surfaces with conical singularities.
method Adapting Volkov's variational method to handle Lorentzian angles.
result Existence of a locally Minkowski 3-manifold with conical singularities isometric to a given surface.
Paper proves inequality for capillary hypersurfaces with new proof.
problem Proving a Heintze-Karcher type inequality for hypersurfaces with capillary boundary.
method Using a mixed boundary value problem in Reilly type formula to establish the inequality.
result New proof of Alexandrov type theorem for capillary hypersurfaces.
We first prove a general gluing theorem which creates new nondegenerate constant mean curvature surfaces by attaching half Delaunay surfaces with small necksize to arbitrary points of any nondegenerate CMC surface. The proof uses the method of Cauchy data matching from \cite{MP}, cf. also \cite{MPP}. In the second part…
Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the spheremath.DG
We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do Carmo-Warner to convex -hypersurfaces. We apply these results to prove -convergence of inverse F-curvature flows in the sphere to an equator in \mathbb{S}^{n+1} for embedde…
We prove an Alexandrov type theorem for a quotient space of . More precisely we classify the compact embedded surfaces with constant mean curvature in the quotient of by a subgroup of isometries generated by a parabolic translation along horocycles of $\mathbb …
Paper proves stable capillary hypersurfaces in balls are totally umbilical.
problem Proving uniqueness of stable capillary hypersurfaces in a ball.
method New Minkowski type formula and Heintze-Karcher-Ros type inequality.
result Proves stable capillary hypersurfaces in a ball are totally umbilical.
The paper improves proximity estimates for hypersurfaces with almost constant curvature in space forms.
problem Proximity to a single sphere for hypersurfaces with curvature functions close to a constant.
method Unified approach using the method of moving planes.
result Sharp quantitative estimates of proximity to a single sphere.
The study examines hypersurfaces close to constant mean curvature and their proximity to spheres.
problem Understanding hypersurfaces close to constant mean curvature and their proximity to spheres.
method Quantitative stability results for hypersurfaces with mean curvature close to a constant.
result Hypersurfaces close to constant mean curvature are closely related to spheres, with quantitative descriptions of proximity.
We construct new constant mean curvature surfaces in H2xR. They arise as sister surfaces of Plateau solutions. It is a family of MC 1/2 surfaces with k ends, genus 1 and k-fold dihedral symmetry, k greater 2. The surfaces are Alexandrov- embedded.
Study null energy condition impacts on special hypersurfaces in static spacetimes.
problem Effects of null energy condition on totally umbilic hypersurfaces.
method Characterization of embedded surfaces and photon surfaces using Alexandrov Theorem and other methods.
result Full characterization of embedded surfaces with constant spacetime mean curvature.
We are concerned with hypersurfaces of with constant nonlocal (or fractional) mean curvature. This is the equation associated to critical points of the fractional perimeter under a volume constraint. Our results are twofold. First we prove the nonlocal analogue of the Alexandrov result characterizing sph…
Unified framework for Alexandrov 3-spaces, extending manifold results.
problem Extend manifold topology results to Alexandrov 3-spaces.
method Generalize connected sum, prime decomposition, and Dehn surgery.
result Unified framework for Alexandrov 3-spaces, including non-manifold spaces.
New stability estimate for spherical symmetry of hypersurfaces with constant mean curvature.
problem Stability of hypersurfaces with constant mean curvature near a sphere.
method Stability estimate using integral identities and inequalities related to torsional rigidity.
result Hypersurfaces can be contained in a spherical annulus with a specific radius difference.
Estimates eigenvalues on differential forms on Alexandrov spaces.
problem Estimating eigenvalues of differential form Laplacians on Alexandrov spaces.
method Using Alexandrov spaces with curvature bounded below, constructing differential form Laplacians, and applying local biLipschitz assumptions.
result The differential form Laplacian has a compact resolvent under local biLipschitz assumption, and its kernel is identified with an intersection homology group.
The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
problem Conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
method Proposes a Gluing Conjecture and proves it under certain conditions.
result The Gluing Conjecture is true under specific conditions, generalizing Petrunin's Gluing Theorem.
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold is actually an isometry with respect to some other, optimal, Riemannian metric . We consider the natural action of volumorphisms on the space $\M_μ^s$ of all Riemannian metrics of Sobolev class , , with a f…
In this paper, we study the space of translational limits T(M) of a surface M properly embedded in R^3 with nonzero constant mean curvature and bounded second fundamental form. There is a natural map T which assigns to any surface M' in T(M), the set T(M') in T(M). Among various dynamics type results we prove that surf…
Constructs 2-convex functions approximating distances in Alexandrov spaces.
problem Distance approximation in finite-dimensional Alexandrov spaces.
method Constructs 2-convex functions in Alexandrov spaces.
result Functions can be lifted to close Alexandrov spaces.
Alexandrov spaces have a special stratification that maps to spheres.
problem Characterizing the structure of Alexandrov spaces.
method Extremal stratification and space of directions analysis.
result Alexandrov spaces are homeomorphic to spheres in their space of directions.
The paper extends an Alexandrov theorem to Minkowski spacetime.
problem Generalizing Alexandrov's theorem to Minkowski spacetime.
method Adapting conditions for closed codimension-two spacelike submanifolds in Minkowski spacetime.
result A generalized Alexandrov theorem for Minkowski spacetime.
We study three-dimensional Alexandrov spaces with a lower curvature bound, focusing on extending three classical results on three-dimensional manifolds: First, we show that a closed three-dimensional Alexandrov space of positive curvature, with at least one topological singularity, must be homeomorphic to the suspensio…
Classifies 4D Alexandrov spaces with torus actions.
problem Classifying Alexandrov spaces with torus actions.
method Equivariant classification and homeomorphism analysis.
result Alexandrov spaces are homeomorphic to Riemannian orbifolds.
Generalizes Toponogov theorem to Alexandrov spaces.
problem Estimating curve length in non-Euclidean spaces.
method Generalization of Toponogov theorem.
result Proved the length of a curve in two-dimensional Alexandrov spaces.
Generalizes a soul-bound for noncompact Alexandrov spaces.
problem Finding a lower bound for injectivity radius in Alexandrov spaces.
method Introduces the soul of Alexandrov spaces and applies a generalized bound.
result Injectivity radius is at least πK⁻¹/² if not equal to the soul's.