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.
A new numerical framework simplifies elastic surface matching and comparison.
The paper defines and proves the existence of decompositions of integral varifolds.
New varifold example shows decomposition failure.
New moving plane method for varifolds promotes smoothness from boundary to interior.
Upper bound for Morse index of min-max varifolds.
Paper provides estimates for varifolds with critical mean curvature.
The paper simplifies arguments for stationary varifolds results.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of…
Generalizes Reilly inequality to varifolds and analyzes equality cases.
Counterexample and new proof for curvature varifolds.
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our var…
Sharp criteria for 2-varifolds to be induced by smooth immersions.
Establishes a boundary maximum principle for varifolds with fixed contact angle.
Sharp lower bound found for integral varifolds' mean curvature.
In this work it is shown that every integral varifold in an open subset of Euclidian space of locally bounded first variation can be covered by a countable collection of submanifolds of class C^2. Moreover, the mean curvature of each member of the collection agrees with the mean curvature of the varifold almost everywh…
New varifolds with capillary boundary properties studied.
Green functions on stationary varifolds established with inequalities and convergence results.
The paper studies the consistency of mean curvature flow via volumetric varifolds.
Proves ε-regularity for capillary surfaces in Riemannian manifolds.
Study quantizes energy distribution in inhomogeneous phase transitions.
Study introduces indecomposability for varifolds, leading to geometric consequences.
The paper proves smoothness of stationary varifolds.
We survey - by means of 20 examples - the concept of varifold, as generalised submanifold, with emphasis on regularity of integral varifolds with mean curvature, while keeping prerequisites to a minimum. Integral varifolds are the natural language for studying the variational theory of the area integrand if one conside…
Study shows distance to boundary is always attained on varifolds with bounded curvature.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
Proves regularity for stable varifolds near specific cones.
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.
The paper proves regularity for varifolds with bounded anisotropic mean curvature.
Bi-Lipschitz proof for 2-varifolds near critical Allard condition.
Proves regularity for stable varifolds near cones, expanding previous work.
We develop a suitable generalization of Almgren's theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in lorentzian m…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts identities for certain compositions with smooth functions. In this class the idea of ze…
The paper proves rigidity estimates for varifolds almost minimizing the Willmore energy.
This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional analytic properties with their Euclidean counterparts. Assuming the varifold to s…
Shows smoothness of varifolds with specific boundary angles.
New varifold solutions for mean curvature flow converge and are unique.
The paper studies surfaces in a bounded domain with orthogonal boundaries and proves curvature estimates.
In this paper we deal with singular varieties of bounded mean curvature in the viscosity sense. They contain all varifolds of bounded generalized mean curvature. In the first part we investigate the second-order properties of these varieties, obtaining results that are new also in the varifold's setting. In particular …
Compactness results for hypersurfaces with mean curvature prescribed by an ambient function.
We give two structural conditions on a codimension integral -varifold with first variation locally summable to an exponent that imply the following: whenever each orientable portion of the -embedded part of the varifold (which is non-empty by the Allard regularity theory) is stationarity and the $C^…
Compact capillary hypersurfaces with specific curvatures are proven.
We prove that every stationary polyhedral varifold minimizes area in the following senses: (1) its area cannot be decreased by a one-to-one Lipschitz ambient deformation that coincides with the identity outside of a compact set, and (2) it is the varifold associated to a mass-minimizing flat chain with coefficients in …
New, shorter proofs for varifolds and flows with improved decay of flatness.
We give a necessary and sufficient geometric structural condition for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth hypersurface away from a small set of generally unavoidable singularities; when this condition is satisfied, the singular set is empty if the…
For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary conditions. In order to show the existence of the limit, we apply the phase field me…
In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.
In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the setting where the mean curvature (of the regular part of the varifold) is prescr…