Entropy for two dimensional extremal black holes is computed explicitly in a finite-space formulation of the black hole thermodynamics and is shown to be zero locally. Our results are in conformity with the recent one by Hawking et al in four dimensions. It is known that black holes have temperature and entropy and are therefore amenable to a thermodynamic description. For an asymptotic observe...

Abstract. The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the BusemannPetty problem, characterizations of intersection bodies, extremal sections of lp-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the resu...

where λ, μ > 0 are parameters and Ω is a smoothly bounded domain of R , N ≥ 1. As shown by M. Montenegro (see [6]), there exists a limiting curve Υ in the first quadrant of the (λ, μ)-plane serving as borderline for existence of classical solutions of (1). He also proved the existence of a weak solution u∗ for every (λ∗, μ∗) on the curve Υ and left open the question of its regularity. Following...

It is shown that every cyclic split system S defined on an n-set with #S > 2kn− (2k+1 2 ) for some k ≤ n−1 2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k, n−(2k+1)) ≤ 3. In addition, some related old and new conjectures are also discussed.

A bstract Using the large D effective theory approach, we construct a static solution of non-extremal and squashed black holes with/without an electric charge, which describes spherical hole in Kaluza-Klein spacetime with compactified dimension. The asymptotic background dimension near-horizon geometry are analytically solved by 1 /D expansion. Particularly, our work demonstrates that limit can...