Harmonic Mappings and Minimal Submanifolds.
Harmonic Maps of the Moduli Space of Compact Riemann Surfaces.
Harmonic morphisms between riemannian manifolds
A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where vanishes. Every non-constant harmonic morphism is shown to be an open mapping....
Harnack Inequalities for Nonuniformly Elliptic Divergence Structure Equations.
Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature
We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
Herissons et multiherissons (enveloppes parametrées par leur application de Gauss)
Higher genus minimal surfaces by growing handles out of a catenoid.
Higher order Codazzi tensors on conformally flat spaces.
Higher order contact of real curves in a real hyperquadric. II
Let be an Hermitian quadratic form, of maximal rank and index , defined over a complex vector space . Consider the real hyperquadric defined in the complex projective space by Let be the subgroup of the special linear group which leaves invariant and the distribution defined by the Cauchy Riemann structure induced over . We study the real regular curves of constant type in , tangent to , finding a complete system of analytic invariants for two curves to be locally equivalent...
Higher order Schwarzian derivatives in interval dynamics
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order, obtaining control over derivatives of high order. For a large class of multimodal interval maps we show that all inverse branches of first return maps to sufficiently small neighbourhoods of critical values have their higher order Schwarzian derivatives positive up...
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Higher-genus Chen-Gackstatter surfaces and the Weierstrass representation for surfaces of infinite genus.
Histoire de la réductibilité du groupe conforme des variétés riemanniennes (1964-1994)
Historický vývoj pojmu křivka [Book]
h-konvexe Kurven in der hyperbolischen Ebene.
Holomorphic Cartan geometries and rational curves
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.
Homogénéité locale pour les métriques riemanniennes holomorphes en dimension
Une métrique riemannienne holomorphe sur une variété complexe est une section holomorphe du fibré des formes quadratiques complexes sur l’espace tangent holomorphe à telle que, en tout point de , la forme quadratique complexe est non dégénérée (de rang maximal, égal à la dimension complexe de ). Il s’agit de l’analogue, dans le contexte holomorphe, d’une métrique riemannienne (réelle). Contrairement au cas réel, l’existence d’une telle métrique sur une variété complexe compacte n’est...
Homogeneous affine hypersurfaces with rank one shape operators.
Homogeneous Cartan geometries
We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal automorphisms. The main result of this paper is that the above calculations are purely algorithmic. As an example of an homogeneous parabolic geometry we treat a conformal structure on the product of two spheres.
Homogeneous parabolic surfaces in .