Related papers: Weakly differentiable functions on varifolds
In this paper we show existence of a trace for functions of bounded variation on Riemannian manifolds with boundary. The trace, which is bounded in $L^\infty$, is reached via $L^1$-convergence and allows an integration by parts formula. We…
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
In the paper, the basic results on boundary trace of the book "Sobolev spaces" by V. Maz'ya are generalized to a wider class of regions. In the book, boundary trace of BV-functions is defined for regions with finite perimeter and the main…
We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
Consider a BV function on a Riemannian manifold. What is its differential? And what about the Hessian of a convex function? These questions have clear answers in terms of (co)vector/matrix valued measures if the manifold is the Euclidean…
This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply…
In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…
The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…
In this article, we investigate the theory of weighted functions of bounded variation (BV), as introduced by Baldi [Ba01]. Depending on the theorem, we impose lower semicontinuity and/or a pointwise A1 condition on the weight. Our…
We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…
The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold $M$ with smooth boundary $\partial M$. Here, we will give the complete classification for an $n$-dimensional, $n=3$ or $4,$…
We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the base of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are…
We present a weakly supervised deep learning method to perform instance segmentation of cells present in microscopy images. Annotation of biomedical images in the lab can be scarce, incomplete, and inaccurate. This is of concern when…
Given matrices $A$ and $B$ such that $B=f(A)$, where $f(z)$ is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of $A$ and $B$. We provide family of bounds which depend on the…
We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…
Our purpose is to state quantitative conditions ensuring the rectifiability of a $d$--varifold $V$ obtained as the limit of a sequence of $d$--varifolds $(V_i)_i$ which need not to be rectifiable. More specifically, we introduce a sequence…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…
Establishing dense correspondences across image pairs is essential for tasks such as shape reconstruction and robot manipulation. In the challenging setting of matching across different categories, the function of an object, i.e., the…