43 citations · 97 across the 8 of their papers we have counts for
9 papers
Spherically symmetric solutions to the Einstein-scalar field conformal constraint equations
Philippe Castillon, Cang Nguyen-The
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in…
Prescribing The Gauss Curvature Of Convex Bodies In Hyperbolic Space
Jérôme Bertrand, Philippe Castillon
The Gauss curvature measure of a pointed Euclidean convex body is a measure on the unit sphere which extends the notion of Gauss curvature to non-smooth bodies. Alexandrov's proble…
A Spectral Characterization Of Geodesic Balls In Non-Compact Rank One Symmetric Spaces
Philippe Castillon, Berardo Ruffini
In constant curvatures spaces, there are a lot of characterizations of geodesic balls as optimal domain for shape optimization problems. Although it is natural to expect similar ch…
Remarks on J. Espinar's "Finite index operators on surfaces"
Pierre Bérard, Philippe Castillon
In this paper, we make some remarks on José Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].
On asymptotically harmonic manifolds of negative curvature
Philippe Castillon, Andrea Sambusetti
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of informa…
Spectral positivity and Riemannian coverings
Pierre Bérard, Philippe Castillon
Let be a complete non-compact Riemannian manifold. We consider operators of the form , where is the non-negative Laplacian associated with the metric , an…