相关论文: Generic Smooth Connection Functions - A New Analyt…

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding…

Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring…

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time.…

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments and requires only one additional quantity to be computed: the length of…

For the minimal graph with strict convex level sets, we find an auxiliary function to study the Gaussian curvature of the level sets. We prove that this curvature function is a concave function with respect to the height of the minimal…

We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular…

We present a fixed-parameter tractable (FPT) algorithm to find a shortest curve that encloses a set of k required objects in the plane while paying a penalty for enclosing unwanted objects. The input is a set of interior-disjoint simple…

This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.

The principal goal of the physics of the fundamental interactions is to provide a consistent description of the nature of the subnuclear forces, which manifest in our universe, together with the gravitational force, in a unified framework.…

The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more…

The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2\pi. This is an extremal length problem in…

We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…

The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring…

Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…

This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…

We are concerned with two interrelated problems: smoothability of connection 1-forms with low regularity on bundles with prescribed smooth curvature 2-forms, and existence of isometric immersions with low regularity. We first show that if…

A novel static algorithm is proposed for numerical reparametrization of periodic planar curves. The method identifies a monitor function of the arclength variable with the true curvature of an open planar curve and considers a simple…

Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to…

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…