A proof of the Chern-Lashof conjecture in dimensions greater than five.
A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary).
A regularity theorem for curvature flows.
A remark about minimal surfaces with flat embedded ends.
A remark on almost umbilical hypersurfaces
In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.
A remark on semi-∇-flat functions
We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).
A Rigidity Theorem for Higher Codimensions.
A rigidity theorem for Riemann's minimal surfaces
We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
A short proof of the minimality of Simons cone
A singular example for the averaged mean curvature flow.
A Singular Solution of the Capillary Equation. I. Existence.
A Singular Solution of the Capillary Equation. II. Uniqueness.
A Singularity Theorem for Twistor Spinors
We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.
A Software for the Visualisationof Differential Geometry
A specialization of an anholonomial subvarietes system of an -dimensional variety in unimodular -dimensional space
A sphere problem in Euclidean space. (Ein Kugelproblem im euklidischen Raum.)
A spherical Fabricius-Bjerre formula with applications to closed space curves.
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
A strong minimax property of nondegenerate minimal submanifolds.
A study on the one parameter Lorentzian spherical motions.