Related papers: On minimal kernels and Levi currents on weakly com…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

In this paper, given a topological space $X$, an interval $I\subseteq {\bf R}$ and five continuous functions $\varphi, \psi, \omega :X\to {\bf R}$, $\alpha, \beta:I\to {\bf R}$, we are interested in the infimum of the function $\Phi:X\to…

We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremum spaces with Lyapunov type functions and local domination.…

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace-Beltrami operator on M. We assume that the kernel associated to…

Consider a second order, strongly elliptic negative semidefinite differential operator $L$ (maybe a system) on a compact Riemannian manifold $\overline{M}$ with smooth boundary, where the domain of $L$ is defined by a coercive boundary…

We prove that, for an arbitrary topological space $X$, the following two conditions are equivalent: (a) Every open cover of $X$ has a finite subset with dense union (b) $X$ is $D$-pseudocompact, for every ultrafilter $D$. Locally, our…

This is a review of electroweak precision physics with particular emphasis on low-energy precision measurements in the neutral current sector of the electroweak theory and includes future experimental prospects and the theoretical…

Let $\varphi$ be a locally upper bounded Borel measurable function on a Greenian open set $\Omega$ in $R^d$ and, for every $x\in \Omega$, let $v_\varphi(x)$ denote the infimum of the integrals of $\varphi$ with respect to Jensen measures…

We introduce the Grassmannian $q$-core of a distribution of subspaces of the tangent bundle of a smooth manifold. This is a generalization of the concept of the core previously introduced by the first two authors. In the case where the…

This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic…

We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable endomorphism field $\phi$. For the normal case, we prove that a $\phi$-invariant submanifold tangent to a Reeb vector field…

Results on the upper and lower semicontinuity of functionals defined on spaces of convex and more general functions are established. In particular, the following result is obtained. Let $\phi(v; \cdot)$ be the density of the absolutely…

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal…

In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function $\varphi$ with an isolated singularity at $0$ in an open subset of ${\mathbb C}^n$. This threshold is defined as the supremum of…

We investigate the operator-theoretic property of strict singularity for optimal Sobolev embeddings within the general framework of rearrangement-invariant function spaces (r.i. spaces). More specifically, we focus on studying the…

We prove a Lipschitz approximation with superlinear error terms for integral currents $\omega$-minimizing the area functional, where $\omega$ is a modulus of continuity satisfying a Dini condition. We also present an almost monotonicity…

This study uses the ideas of \cite{Rieffel} to provide the dual of $L^1(\mu,X)$ in the positive and $\sigma-$ finite cases. This results in elegant necessary and sufficient criteria for weak compactness in $L^1(S,\mu,X)$ in the…

This work is a complement of the study on H\"ormander's solution of the $\bar\partial$ equation initialised by H. Hedenmalm. Let $\varphi$ be a strictly plurisubharmonic function of class C 2 in C n, let $c_\varphi(z)$ be the smallest…