Related papers: Some recent applications of the barycenter method …
In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.
The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…
Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements. In this paper we…
In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of complex models arising in mathematical physics. These results…
This paper is the first in a series of two articles whose aim is to extend a recent result of Guillarmou-Lefeuvre on the local rigidity of the marked length spectrum from the case of compact negatively-curved Riemannian manifolds to the…
The present work extends the direct-forcing immersed boundary method introduced by Garc\'ia-Villalba et al. (2023), broadening its application from spherical to arbitrarily-shaped particles, while maintaining its capacity to address both…
Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be…
This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow…
In this paper, we generalize the simple Euclidean 1-center approximation algorithm of Badoiu and Clarkson (2003) to Riemannian geometries and study accordingly the convergence rate. We then show how to instantiate this generic algorithm to…
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…
This paper is concerned with the problem of defining and estimating statistics for distributions on spaces such as Riemannian manifolds and more general metric spaces. The challenge comes, in part, from the fact that statistics such as…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
We present a novel barycentric interpolation algorithm designed for analytic functions $f\in\mathcal{A}(E)$ defined on the complex plane. The algorithm, which encompasses both polynomial and rational interpolation, is tailored to handle…
More than ten years ago Ikehata discovered two mathematical methods for the purpose of extracting information about the location and shape of unknown discontinuity embedded in a known background medium from observation data. The methods are…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
A novel surface correction method is proposed for bond based peridynamics which ensures energy consistency with a classical reference body for general affine deformations. This method is validated for simple geometries and then applied to a…
We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: asymptotic parameters, improved estimates on the minimum…
A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…