On the - theorems
On the geometry of convex reflectors
In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such inverse problem...
On the -theorem for hypersurfaces
On the non-existence of certain ovaloids
On the Pick invariant
On Weingarten surfaces
Order of holonomy of a surface with projective connection
Ovaloids with prescribed curvature of the second fundamental form
Plongements radiaux à courbure de Gauss positive prescrite
Pointed -surfaces
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces
A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly one convex...
Properties of distance functions on convex surfaces and applications
If is a convex surface in a Euclidean space, then the squared intrinsic distance function is DC (d.c., delta-convex) on in the only natural extrinsic sense. An analogous result holds for the squared distance function from a closed set . Applications concerning -boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given.
Réalisations globalement régulières de disques strictement convexes dans les espaces d'Euclide et de Minkowski par la méthode de Weingarten
Remark on a conjectured characterization of the sphere
Remark on surfaces in satisfying certain relations between covariant derivatives of the mean and Gauss curvatures
Remark to the characterization of the sphere in
Remarks on Chebyshev coordinates.
Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps
This paper is a study of harmonic maps fromRiemannian polyhedra to locally non-positively curved geodesic spaces in the sense of Alexandrov. We prove Liouville-type theorems for subharmonic functions and harmonic maps under two different assumptions on the source space. First we prove the analogue of the Schoen-Yau Theorem on a complete pseudomanifolds with non-negative Ricci curvature. Then we study 2-parabolic admissible Riemannian polyhedra and prove some vanishing results on them.
Riemannsche Flächen mit Eigenwerten in (0, ...).
Rigidity and Energy.