We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this ...

We prove some asymptotic interior regularity results for potential functions of optimal transportation problems with power costs. We show that our problems are equivalent to optimal transportation problems whose cost ...

In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences ...

In this paper we analyze the global existence of classical solutions to the initial boundaryvalue problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations ...

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Ca arelli-Silvestre and a class of conformally covariant operators in conformal geometry.

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry.

We prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonz alez and Qing. These are inspired ...