Related papers: Non-Lipschitz uniform domain shape optimization in…

In relatively nice geometric settings, in particular, on Lipschitz domains, absolute continuity of elliptic measure with respect to the surface measure is equivalent to Carleson measure estimates, to square function estimates, and to…

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed…

The purpose of this paper is to provide a detailed description of the spaces that can be specified as $L^2$ domains for the operators of a first order elliptic complex on a compact manifold with conical singularities. This entails an…

In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover,…

In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…

The well-known von Bahr--Esseen bound on the absolute $p$th moments of martingales with $p\in(1,2]$ is extended to a large class of moment functions, and now with a best possible constant factor (which depends on the moment function). This…

In this paper we extend to non-compact Riemannian manifolds with boundary the use of two important tools in the geometric analysis of compact spaces, namely, the weak maximum principle for subharmonic functions and the integration by parts.…

We give a short proof that any non-zero Euclidean space has a compact subset of Hausdorff dimension one that contains a differentiability point of every real-valued Lipschitz function defined on the space.

We prove that there exists a bounded convex domain $\Omega \subset \mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain…

We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…

The main result of this paper is that the space of conformally compact Einstein metrics on a given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We…

The weak well-posedness results of the strongly damped linear wave equation and of the non linear Westervelt equation with homogeneous Dirichlet boundary conditions are proved on arbitrary three dimensional domains or any two dimensional…

We prove two types of nodal results for density one subsequences of an orthonormal basis $\{\phi_j\}$ of eigenfunctions of the Laplacian on a negatively curved compact surface. The first type of result involves the intersections $Z_{\phi_j}…

We prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Hausdorff propinquity. In particular, our result applies to…

We study the behavior under Gromov-Hausdorff convergence of the spectrum of weighted $\barpartial$-Laplacian on compact K\"ahler manifolds. This situation typically occurs for a sequence of Fano manifolds with anticanonical K\"ahler class.…

We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand…

This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing…

The goal of the paper is to give an optimal transport characterization of sectional curvature lower (and upper) bounds for smooth $n$-dimensional Riemannian manifolds. More generally we characterize, via optimal transport, lower bounds on…

We show that the Hausdorff dimension of the singular set of perimeter minimizers in non-collapsed Ricci limit spaces with a two-sided Ricci curvature bound is at most $N-5$, where $N$ is the dimension of the ambient space. The estimate is…

We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n=1}^\infty \frac{1}{a_n b_n}$, where $b_n$ satisfies some growth condition and $a_n$ lies in some set, possibly…