Related papers: On the Mobius function of a lower Eulerian Cohen-M…
We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as the determinant vanishes. This notion, that we call…
We show that, over a local complete intersection, every possible variety is realized as the cohomological support variety of some module. Moreover, we show that the projective variety of a complete indecomposable maximal Cohen-Macaulay…
The result in the title is proven, using the Selberg estimate on the leading eigenvalue of the non-Euclidean Laplacian, and the method of conformal volumes of Li and Yau.
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…
We consider the action of a real reductive group G on a Kaehler manifold Z which is the restriction of a holomorphic action of the complexified group G^C. We assume that the induced action of a compatible maximal compact subgroup U of G^C…
We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. This includes as special cases Quillen's plus…
Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive…
In this paper, we consider Poincar\'e inequalities for non euclidean metrics on $\mathbb{R}^d$. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for…
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the…
Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for quasiconvex (level-set convex) Hamiltonians not necessarily…
Motivated by Talagrand's conjecture on regularization properties of the natural semigroup on the Boolean hypercube, and in particular its continuous analogue involving regularization properties of the Ornstein-Uhlenbeck semigroup acting on…
We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's…
We study the connection between the concavity properties of a measure $\nu$ and the convexity properties of the associated relative entropy $D(\cdot \Vert \nu)$ along optimal transport. As a corollary we prove a new dimensional…
This note describes sharp Milnor--Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperbolic planes. One consequence is that such manifolds do not…
We present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are positivity improving (and hence ergodic) with…
The AH conjecture relates the low-dimensional homology groups of a groupoid with the abelianization of its topological full group. We show that transformation groupoids of minimal actions of the infinite dihedral group on the Cantor set…
We study the Sobolev inequality and the existence of its extremal functions in the setting of homogeneous H\"{o}rmander vector fields. A principal result establishes a mutual inclusion between the set of volume growth rates of subunit balls…
The Riesz-Sobolev inequality provides an upper bound for a trilinear expression involving convolution of indicator functions of sets. It is known that equality holds only for homothetic ordered triples of appropriately situated ellipsoids.…
We exhibit some strong positivity properties of a certain function which implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset…
In this paper, we study the topological structure of the Hahn field whose elements are functions from the additive abelian group of rational numbers to the real numbers field, with well-ordered support. After reviewing the algebraic and…