Related papers: The Penrose Inequality for Metrics with Singular S…
What happens at spacetime singularities is poorly understood. The Penrose-Wall singularity theorem constrains possible scenarios, but until recently its key assumption--the generalized second law (GSL)--had only been proven perturbatively,…
In this paper, we mainly study metric subregularity for a convex constraint system defined by a convex set-valued mapping and a convex constraint subset. The main work is to provide several primal equivalent conditions for metric…
Motivated by the work of Li and Mantoulidis, we study singular metrics which are uniformly Euclidean $(L^\infty)$ on a compact manifold $M^n$ ($n\ge 3$) with negative Yamabe invariant $\sigma(M)$. It is well-known that if $g$ is a smooth…
In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres…
An old conjecture of Durfee 1978 bounds the ratio of two basic invariants of complex isolated complete intersection surface singularities: the Milnor number and the singularity (or geometric) genus. We give a counterexample for the case of…
A hypersurface without umbilics in the n+1 dimensional Euclidean space is known to be determined by the Moebius metric and the Moebius second fundamental form up to a Moebius transformation when n>2. In this paper we consider Moebius…
This is a report of a joint work with E. J\"arvenp\"a\"a, M. J\"arvenp\"a\"a, T. Rajala, S. Rogovin, and V. Suomala. In [3], we characterized uniformly porous sets in $s$-regular metric spaces in terms of regular sets by verifying that a…
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have…
We prove the spacetime Penrose inequality for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer…
We find a Penrose limit of AdS_5 x T^{1,1} which gives the pp-wave geometry identical to the one that appears in the Penrose limit of AdS_5 x S^5. This leads us to conjecture that there is a subsector of the corresponding N=1 gauge theory…
Roger Penrose's 2020 Nobel Prize in Physics recognises that his identification of the concepts of "gravitational singularity" and an "incomplete, inextendible, null geodesic" is physically very important. The existence of an incomplete,…
In this paper we investigate the extension of the charged Riemannian Penrose inequality to the case where charges are present outside the horizon. We prove a positive result when the charge densities are compactly supported, and present a…
In $L^2$ extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of…
This article is the sequel to our previous paper [LS] dealing with the near-equality case of the Positive Mass Theorem. We study the near-equality case of the Penrose Inequality for the class of complete asymptotically flat rotationally…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a description as an infra-red fixed point obtained by deforming the N=4 supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral multiplets. We…
The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity…
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some general tensor, which are all the tensors that admit those same…