arXiv research

New optimal isosystolic inequality found for Finsler reversible 2-tori.

In this paper, the isoperimetric problem in the 2-dimensional Finsler space form $(F_B,B^2(1))$ with k = 0 by using the Busemann-Hausdorff area is investigated. We prove that the circle centered the origin achieves the local maximum area of the isoperimetric problem.

We explore a connection between the Finslerian area functional based on the Busemann-Hausdorff-volume form, and well-investigated Cartan functionals to solve Plateau's problem in Finsler 3-space, and prove higher regularity of solutions. Free and semi-free geometric boundary value problems, as well as the Douglas probl…

Study weakly weighted Einstein-Finsler metrics, showing specific curvature properties and characterizing them.

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen's S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.

The paper proposes extensions of the usual notions of Finslerian volume to time orientable Finsler spacetime manifolds. The basic idea is to replace, in the classical Busemann-Hausdorff and Holmes-Thompson definitions, integration on the indicatrices of the given metric (which are, in Lorentzian signature, non-compact,…

The contribution of this paper is two-fold. The first one is to derive a simple formula of the mean curvature form for a hypersurface in the Randers space with a Killing field, by considering the Busemann-Hausdorff measure and Holmes-Thompson measure simultaneously. The second one is to obtain the explicit local expres…

Given a Finsler manifold $(M,F)$, it is proved that the first eigenvalue of the Finslerian $p$-Laplacian is bounded above by a constant depending on $\ p$, the dimension of $M$, the Busemann-Hausdorff volume and the reversibility constant of $(M,F)$. For a Randers manifold $(M,F:=\sqrt{g}+β)$, where $g$ is a Riemannian…

Study on Berwald-Weyl curvature with projective invariance and vanishing results.

NeuroPaint infers missing brain area dynamics from multi-animal datasets.

In this paper, we introduce the $L_p$ geominimal surface area for all $-n\neq p<1$, which extends the classical geominimal surface area ($p=1$) by Petty and the $L_p$ geominimal surface area by Lutwak ($p>1$). Our extension of the $L_p$ geominimal surface area is motivated by recent work on the extension of the $L_p$ a…

Overview of affine surface area and its history.

Hasse principle applied to area-minimizing submanifolds across different homology types.

Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for $L_φ$ affine surface areas are established.

The hermitian analog of Aleksandrov's area measures of convex bodies is investigated. A characterization of those area measures which arise as the first variation of unitarily invariant valuations is established. General smooth area measures are shown to form a module over smooth valuations and the module of unitarily …

BiLipschitz mappings can be extended to preserve area.

Formula for Heisenberg group surface areas derived.

Introduces new weighted floating functions and affine surface areas.

Study minimal annuli in a slab, estimating their area.

Study area-minimizing subgraphs in integer lattices.

Existing attention mechanisms are trained to attend to individual items in a collection (the memory) with a predefined, fixed granularity, e.g., a word token or an image grid. We propose area attention: a way to attend to areas in the memory, where each area contains a group of items that are structurally adjacent, e.g…

Upper bounds on area for surfaces with constant mean curvature in hyperbolic 3-manifolds.

Study shows area-minimizing submanifolds are mostly rough, not smooth.

Minimal surfaces in hyperbolic space have a renormalized area criterion.

Study examines Hilbert area of inscribed polygons in projective geometry.

Minimal area of spun trefoil knot is found in 4D cubical space.

We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension.

We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same boundary values.

The paper connects least area surfaces to quasi-normal surfaces in 3-manifolds.

Pedal curves derived from ellipses are invariant in area.

We prove the existence of a continuous $BV$ minimizer with $C^{0}$ boundary value for the $p$-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from $BV$ functions to vector-valued measures. Our main purpose is to study the first and second v…

Contracts for Difference (CfDs) are forwards on the spread between an area price and the system price. Together with the system price forwards, these products are used to hedge the area price risk in the Nordic electricity market. The CfDs are typically available for the next two months, three quarters and three years.…

Random forests and LASSO methods improve small area estimation using auxiliary data.

Generalized Cauchy's surface area formula to arbitrary submanifolds in R^n.

Study area minimizing currents in conformal cones, solving Dirichlet problems.

Paper proves existence of area-minimizing submanifolds on almost any manifold with fractal singular sets.

The study finds conditions for area-minimizing cones over submanifolds.

For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its spherical floating body is investigated. This gives rise to a new spherical area measure, the floating area. Remarkably, this floating area…

The paper proves rigidity theorems for area widths of Riemannian manifolds.

Study of large area-constrained Willmore surfaces in Schwarzschild-like manifolds.

The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an …

Study calculates the renormalized area of catenoids in hyperbolic spaces.

Study on existence and structure of P-area surfaces in Heisenberg group.

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate…

New minimal surfaces can have huge area and index.

In this paper, by constructing area-nonincreasing retractions, we prove area-minimizing properties of some cones over minimal embeddings of R-spaces.

Classifies area-minimizing surfaces in R^4 as algebraic.

Sharp lower bound found for area of vector fields on spherical annuli.