Related papers: A Rough Divergence Theorem
We develop a general boundary calculus for algebraic phases and use it to formulate an intrinsic structural framework for deformation and obstruction phenomena. Structural boundaries are shown to be finitely detectable and canonically…
In this paper the generalized Radon transform over level hypersurfaces of CES-functions of measures supported in positive orthant is studied. A characterization of the generalized Radon transform of nonnegative measures is found. Explicit…
The classical Mazur-Ulam theorem establishes that every surjective isometry between normed real vector spaces is an affine transformation. In various applied mathematical settings, however, one encounters maps that preserve distances not…
We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain rather than the first one. This bound is amenable to…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tensor representations, leading to impractically high-dimensional…
We consider the vector functions in a domain homeomorphic to a spherical layer bounded by twice continuously differentiable surfaces. Additional restrictions are imposed on the domain, which allow to conduct proofs using simple methods. On…
In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…
We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under very mild hypotheses.
Capacities of generalized condensers are applied to prove a two-point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robin capacity with respect to the domain of definition of the…
We give necessary and sufficient conditions for the existence of a generalization of R\'enyi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $\mu$ is non-atomic, we found that not all…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
There is the classical Radon theorem. Given integer $d \geq 1$ and $d+2$ points in d-dimensional space $R^d$. Then these points can be divided into two disjoint subsets whose convex hulls have a non-empty intersection. The original proof of…
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its…
The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of black holes, the formation of trapped…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and non-Lipschitz curves. That is, while the…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
A comparison theorem for the isoperimetric profile on the universal cover of surfaces evolving by normalised Ricci flow is proven. For any initial metric, a model comparison is constructed that initially lies below the profile of the…
The need for efficient normal integration methods is driven by several computer vision tasks such as shape-from-shading, photometric stereo, deflectometry, etc. In the first part of this survey, we select the most important properties that…