arXiv research

Solves capillary $L_p$-Christoffel-Minkowski problem in half-space.

Paper solves Christoffel-Minkowski problem in hyperbolic space.

Unified flow solves $L^p$ Christoffel-Minkowski problem for $p>1$.

The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.

Paper studies inverse curvature flows and solves related geometric problems.

New capillary Christoffel-Minkowski problem solved for half-space.

This paper optimizes sampling for least-squares approximation.

Outlier detection methods have become increasingly relevant in recent years due to increased security concerns and because of its vast application to different fields. Recently, Pauwels and Lasserre (2016) noticed that the sublevel sets of the inverse Christoffel function accurately depict the shape of a cloud of data …

New flow method solves Christoffel-Minkowski problem.

Solves Christoffel problem for disk area measures on spheres.

Solves Christoffel-Minkowski problem and Hessian equations with radial symmetry.

Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nyström approximations based on the selection or sampling of landmarks. In this context, …

Directly proves Brioschi formula for Gaussian curvature.

We investigate the relation between quadrics and their Christoffel duals on the one hand, and certain zero mean curvature surfaces and their Gauss maps on the other hand. To study the relation between timelike minimal surfaces and the Christoffel duals of 1-sheeted hyperboloids we introduce para-holomorphic elliptic fu…

Improves data-driven reachability estimation for complex systems.

This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.

Paper solves Christoffel-Minkowski and Weingarten curvature problems in hyperbolic space.

We consider a fully nonlinear partial differential equation associated to the intermediate $L^p$ Christoffel-Minkowski problem in the case $1<p<k+1$. We establish the existence of convex body with prescribed $k$-th even $p$-area measure on $\mathbb S^n$, under an appropriate assumption on the prescribed function. We co…

In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel symbol.

Christoffel function characterizes the corruption a bounded-degree certificate cannot remove in robust halfspace learning.

Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature. Yet, the very nature of this quantity is barely understood. Borrowing ideas from the orthogonal polynomial literature, we in…

Study solves a generalized Christoffel-Minkowski problem using curvature flow.

Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.

A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For $n$ dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that…

Solves Christoffel-Minkowski problem for capillary convex bodies in Euclidean half-space.

The article approximates solutions to the Beltrami equation using similarity surfaces.

Log-concave coefficient sequences for two-bridge knots proved.

Solves Christoffel-Minkowski problem for axially symmetric bodies.

Paper solves a geometric problem involving mixtures of area and curvature measures.

Improved function approximation for noisy data.

The execution flow drives market dynamics, validated on real data.

Our first objective in this paper is to give a natural formulation of the Christoffel problem for hypersurfaces in $H^{n+1}$, by means of the hyperbolic Gauss map and the notion of hyperbolic curvature radii for hypersurfaces. Our second objective is to provide an explicit equivalence of this Christoffel problem with t…

The space of polygons up to similarity is studied using the Schwarz-Christoffel formula.

Author finds the solutions of the Christoffel problem for open and closed surfaces in Riemannian space. The Christoffel problem is reduced to the problem of construction the continuous G-deformations preserving the sum of principal radii of curvature for every point of surface in Riemannian space. G-deformation transfe…

We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_k is the k-th symmetric polynomial of the principle curvature …

Derives Levi-Civita connection formulas for specific geometries.

Type A surfaces are the locally homogeneous affine surfaces which can be locally described by constant Christoffel symbols. We address the issue of the geodesic completeness of these surfaces: we show that some models for Type A surfaces are geodesically complete, that some others admit an incomplete geodesic but model…

In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann-Christoffel curvature tensor, the same type structure given by imposing same restriction on other curvature tensors being studied. The main object of the present paper is to study the equivalency of various ge…

Derives a formula for the k-th covariant derivative of tensor fields.

The paper studies a flow of convex hypersurfaces using anisotropic curvature functions.

We study Christoffel and Darboux transforms of discrete isothermic nets in 4-dimensional Euclidean space: definitions and basic properties are derived. Analogies with the smooth case are discussed and a definition for discrete Ribaucour congruences is given. Surfaces of constant mean curvature are special among all iso…

We introduce a particular class of unbounded closed convex sets of $\R^{d+1}$, called F-convex sets (F stands for future). To define them, we use the Minkowski bilinear form of signature $(+,...,+,-)$ instead of the usual scalar product, and we ask the Gauss map to be a surjection onto the hyperbolic space $\H^d$. Impo…

Study curvature properties in special manifolds using specific tensors.

New proof shows origin-centred balls are unique solutions to curvature problems.

We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christoffel, Darboux, Bianchi and others, to the more general context of submanifolds of symmetric $R$-spaces with essentially no loss of integrable structure.

Global isothermic immersions are defined and studied with the aid of a connection between quadratic differentials and immersions. The applications are two problems stemming from the fundamental question: how much data is needed to identify a surface immersion (Christoffel's problem) or its shape (Bonnet's problem). A s…

In this paper, we study the inverse surfaces in 3-dimensional Euclidean space $\mathbb{E}^{3}$. We obtain some results relating Christoffel symbols, the normal curvatures, the shape operators and the third fundamental forms of the inverse surfaces

We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a Königs dual in a concentric quadric.