相关论文: Reconstruction of Centrally Symmetrical Convex Bod…

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…

We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are…

High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to spherical, Euclidean and…

We show that if $d\ge 4$ is even, then one can find two essentially different convex bodies such that the volumes of their maximal sections, central sections, and projections coincide for all directions.

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…

We disprove a conjecture of A. Koldobsky asking whether it is enough to compare $(n-2)$-derivatives of the projection functions of two symmetric convex bodies in the Shephard problem in order to get a positive answer in all dimensions.

We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…

This paper continues the study of a class of compact convex hypersurfaces in Euclidean space $R^{n+1}, ~n \geq 1$, which are boundaries of compact convex bodies obtained by taking the intersection of (solid) confocal paraboloids of…

A recent article by Li and Lv considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in cases where the speed is a function of a…

We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.

We propose a new algorithm for approximating the metric projection onto a superelliptic disk of order $p>1$, i.e., the convex hull of a superellipse (Lam\'e curve), and prove its convergence.

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…

We construct a compact convex generating set $\mathcal{C}_n$ of the moduli set of closed connected projective special real manifolds of fixed dimension $n$. We show that a closed connected projective special real manifold corresponds to an…

Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.

X-ray tomography has been studied in various fields. Although a great deal of effort has been directed at reconstructing the projection image set from a rigid-type specimen, little attention has been addressed to the reconstruction of…

We show that the boundary curves (profiles) in $\R^2$ of the generalized projections of a body in $\R^3$ uniquely determine a large class of shapes, and that sparse profile data, combined with projection volume (brightness) data, can be…

A new proof of the Wulff-Gage isoperimetric inequality for origin-symmetric convex bodies is provided. As its applications, we prove the uniqueness of log-Minkowski problem and a new proof of the log-Minkowski inequality of curvature…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…