Related papers: The Hopf Boundary Point Lemma for Vector Bundle Se…

For any vector bundle, we define an inverse system of spectra. In the case of a trivial bundle over a point, the homotopy groups of the filtration quotients give rise to the stable EHP spectral sequence, as was shown by Mahowald. The limit…

In the present paper we prove estimates on {subsolutions of the equation $-Av+c(x)v=0$}, $x\in D$, where $D\subset \bbR^d$ is a domain (i.e. an open and connected set) and $A$ is an integro-differential operator of the Waldenfels type,…

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…

In 2006, Arveson resolved a long-standing problem by showing that for any element $x$ of a separable self-adjoint unital subspace $S\subseteq B(H)$, $\|x\|=\sup\|\pi(x)\|$, where $\pi$ runs over the boundary representations for $S$. Here we…

In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis…

We prove antisymmetric maximum principles and Hopf-type lemmas for linear problems described by the Logarithmic Laplacian. As application, we prove the symmetry of solutions for semilinear problems in symmetric sets, and a rigidity result…

In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For…

We compute the cohomology spaces for the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme H of subschemes of length n of a smooth projective surface X. We show that for L and A invertible vector bundles on X,…

We will generalize a Maximum Principle at Infinity in the parabolic case given by De Lima [Ann. Global Anal. Geom. ${\bf 20}$, 325-343 2001] and De Lima and Meeks [Indiana Univ. Math. Journal ${\bf 53}$ 5, 1211-1223 2004], for disjoints…

A new type of Hopf invariant is described for the fiber of the pinch map from the mapping cone of a map from A to X onto to the suspension of A; this is then used to study the boundary map in the fibration sequence of Cohen, Moore and…

A bounded curvature path is a continuously differentiable piecewise $C^2$ path with a bounded absolute curvature that connects two points in the tangent bundle of a surface. In this work, we analyze the homotopy classes of bounded curvature…

We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower…

We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the…

The sub-Finslerian geometry means that the metric $F$ is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian…

We consider homomorphisms of hermitian holomorphic Hilbert bundles. Assuming the homomorphism decreases curvature, we prove that its pointwise norm is plurisubharmonic.

The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asserts that the family of independent sets of every uniform…

In this article, for singular hermitian metrics on holomorphic vector bundles, we consider minimal $L^2$ integrals on sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds related to modules at boundary…

Suppose that T_t is a symmetric diffusion semigroup on L^2(X) and consider its tensor product extension to the Bochner space L^p(X,B), where B belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the…

We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by…

This survey provides a description of the history and the state of the art of one of the most important fields in the qualitative theory of elliptic partial differential equations including the strong maximum principle, the boundary point…