The laplacian on asymptotically flat manifolds and the specification of scalar curvature
The Legendre transformation
The length spectrum of riemannian two-step nilmanifolds
The Lie derivative and cohomology of -structures.
The Lie structure of C* and Poisson algebras
The local moduli of Sasakian 3-manifolds.
The local structure of essentially conformally symmetric manifolds with constant fundamental function I. The elliptic case
The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian
This paper discusses the question whether the discrete spectrum of the Laplace-Beltrami operator is infinite or finite. The borderline-behavior of the curvatures for this problem will be completely determined.
The magnetic geodesic flow on a homogeneous symplectic manifold.
The maximum principle at infinity for minimal surfaces in flat three manifolds.
The mean curvature measure
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...
The mean curvature of a Lipschitz continuous manifold
The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of is the weak limit (in the sense of distributions) of the mean...
The mean curvature of the second fundamental form of a hypersurface.
The Modular Torus has Maximal Length Spectrum.
The moduli space of special lagrangian submanifolds
The Morse landscape of a riemannian disk
We study upper bounds on the length functional along contractions of loops in Riemannian disks of bounded diameter and circumference. By constructing metrics adapted to imbedded trees of increasing complexity, we reduce the nonexistence of such upper bounds to the study of a topological invariant of imbedded finite trees. This invariant is related to the complexity of the binary representation of integers. It is also related to lower bounds on the number of points in level sets of a real-valued...
The Nash-Kuiper process for curves
A strictly short embedding is an embedding of a Riemannian manifold into an Euclidean space that strictly shortens distances. From such an embedding, the Nash-Kuiper process builds a sequence of maps converging toward an isometric embedding. In that paper, we describe this Nash-Kuiper process in the case of curves. We state an explicit formula for the limit normal map and perform its Fourier series expansion. We then adress the question of Holder regularity of the limit map.
The natural operators lifting connections to higher order cotangent bundles
We prove that the problem of finding all -natural operators lifting classical linear connections on -manifolds into classical linear connections on the -th order cotangent bundle of can be reduced to the well known one of describing all -natural operators sending classical linear connections on -manifolds into tensor fields of type on .
The Nonexistence of Certain Topological Polygons.
The Nonlinear Connections and Harmonicity.