280 research outputs found
The Monge problem in Wiener Space
We address the Monge problem in the abstract Wiener space and we give an
existence result provided both marginal measures are absolutely continuous with
respect to the infinite dimensional Gaussian measure {\gamma}
Monge's transport problem in the Heisenberg group
We prove the existence of solutions to Monge transport problem between two
compactly supported Borel probability measures in the Heisenberg group equipped
with its Carnot-Caratheodory distance assuming that the initial measure is
absolutely continuous with respect to the Haar measure of the group
Two problems related to prescribed curvature measures
Existence of convex body with prescribed generalized curvature measures is
discussed, this result is obtained by making use of Guan-Li-Li's innovative
techniques. In surprise, that methods has also brought us to promote
Ivochkina's estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo
Collapsing Shells and the Isoperimetric Inequality for Black Holes
Recent results of Trudinger on Isoperimetric Inequalities for non-convex
bodies are applied to the gravitational collapse of a lightlike shell of matter
to form a black hole. Using some integral identities for co-dimension two
surfaces in Minkowski spacetime, the area of the apparent horizon is shown
to be bounded above in terms of the mass by the , which is
consistent with the Cosmic Censorship Hypothesis. The results hold in four
spacetime dimensions and above.Comment: 16 pages plain TE
Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
The thermodynamic properties of the (2+1)-dimensional non-rotating black hole
of Ba\~nados, Teitelboim and Zanelli are discussed. The first quantum
correction to the Bekenstein-Hawking entropy is evaluated within the on-shell
Euclidean formalism, making use of the related Chern-Simons representation of
the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum
correction are dealt with a renormalization of the Newton constant. It is
argued that the quantum correction due to the gravitational field shrinks the
effective radius of a hole and becomes more and more important as soon as the
evaporation process goes on, while the area law is not violated.Comment: 14 pages, Latex, one new reference adde
A compactness theorem for scalar-flat metrics on manifolds with boundary
Let (M,g) be a compact Riemannian manifold with boundary. This paper is
concerned with the set of scalar-flat metrics which are in the conformal class
of g and have the boundary as a constant mean curvature hypersurface. We prove
that this set is compact for dimensions greater than or equal to 7 under the
generic condition that the trace-free 2nd fundamental form of the boundary is
nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential
Equation
Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents
Motivated by the statistical mechanics description of stationary
2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity,
we construct a concentrating solution sequence in the form of a tower of
singular Liouville bubbles, each of which has a different degeneracy exponent.
The asymmetry parameter corresponds to the ratio between the
intensity of the negatively rotating vortices and the intensity of the
positively rotating vortices. Our solutions correspond to a superposition of
highly concentrated vortex configurations of alternating orientation; they
extend in a nontrivial way some known results for . Thus, by
analyzing the case we emphasize specific properties of the
physically relevant parameter in the vortex concentration phenomena
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