Related papers: P.d.e.'s which imply the Penrose conjecture

A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between…

We investigate axially symmetric asymptotically flat vacuum self-gravitating system. A class of initial data with apparent horizon was numerically constructed. The examined solutions satisfy the Penrose inequality. The prior analysis of a…

We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they…

This paper is dedicated to the differential Galois theory in the complex analytic context for Lie-Vessiot systems. Those are the natural generaliza- tion of linear systems, and the more general class of differential equations adimitting…

In the theory of submanifolds, the following problem is fundamental: to establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of the submanifolds.The basic relationships discovered until now…

A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…

We present several generalizations of Cauchy's determinant and Schur's Pfaffian by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previuos formulae due to S.Okada…

Motivated by the rigidity case in the localized Riemannian Penrose inequality, we show that suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality is necessarily smooth in properly specified coordinates.…

We reformulate the Generalized Proudman--Johnson (GPJ) equation with parameter a in Lagrangian variables, where it takes the form of an inhomogeneous Liouville equation. This allows us to provide an explicitformula for the flow map, up to…

Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture of general reltivity.

We formulate a conjecture classifying algebraic solutions to (possibly non-linear) algebraic differential equations, in terms of the primes appearing in the denominators of the coefficients of their Taylor expansion at a non-singular point.…

We explain the concepts of computational statistical physics which have proven very helpful in the study of Yang-Mills integrals, an ubiquitous new class of matrix models. Issues treated are: Absolute convergence versus Monte Carlo…

We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generalizes a formula that the first and third authors previously…

In one complex variable, the existence of a compactly supported solution to the Cauchy-Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via…

We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic strategy makes use of the concepts of localization and…

For self-similar sets $X,Y\subseteq \mathbb{R}$, we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining…

We propose a generalisation of the Cameron-Erdos conjecture for sum-free sets to arbitrary non-translation invariant linear equations over Z in three or more variables and, using well-known methods from graph theory, prove a weak form of…

Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…

It is shown that the timelike, spacelike and null versions of the Ehlers identity, as well as ensuing Raychaudhuri equations, might be all derived within a single geometrical approach based on the definition of the Riemann curvature tensor…

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the…