Global geometric structures associated with dynamical systems admitting normal shift of hypersurfaces in Riemannian manifolds.
Global Gronwall estimates for integral curves on Riemannian manifolds.
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Global minimizers for axisymmetric multiphase membranes
We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...
Global models of Riemannian metrics.
In this paper we give certain Riemannian metrics on the manifolds Sn-1 x S1 and Sn (n ≥ 2), which have the property to determine these manifolds, up to diffeomorphisms.The global expressions used for Riemannian metrics are based on the global expression for exterior forms studied in [4]. In [3] one finds certain metrics using global expressions that differ from the type we propose.To some extent, Theorem 3 is a generalization for metrics in an arbitrary dimension, of a theorem proved in [2] for...
Global Pinching Theorems for Even Dimensional Minimal Submanifolds in the Unit Sphere.
Global pinching theorems for minimal submanifolds in spheres
Let M be a compact submanifold with parallel mean curvature vector embedded in the unit sphere . By using the Sobolev inequalities of P. Li to get estimates for the norms of certain tensors related to the second fundamental form of M, we prove some rigidity theorems. Denote by H and the mean curvature and the norm of the square length of the second fundamental form of M. We show that there is a constant C such that if , then M is a minimal submanifold in the sphere with sectional curvature...
Global pinching theorems of submanifolds in spheres.
Globale Invarianten von Raumkurven, Regelflächen und Geradenkongruenzen im einfach isotropen Raum.
Globale Riemannsche Geometrie.
Globale Tschebyscheff-Netze auf Riemannschen Mannigfaltigkeiten und Fortsetzung von Flächen konstanter negativer Krümmung
Globally hyperbolic Lorentzian spaces with special holonomy groups.
Graded lagrangian submanifolds
Graded Poisson structures on the algebra of differential forms.
Gradient estimates for inverse curvature flows in hyperbolic space
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface....
Gradient horizontal de fonctions polynomiales
Nous étudions les trajectoires du gradient sous-riemannien (appellé horizontal) de fonctions polynômes. Dans ce cadre l’inégalité de Łojasiewicz n’est pas valide et une trajectoire du gradient horizontal peut être de longueur infinie, et peut même s’accumuler sur une courbe fermée. Nous montrons que ces comportement sont exceptionnels ; et que, pour une fonction générique les trajectoires de son gradient horizontal ont des propriétés similaires au cas du gradient riemannien. Pour obtenir la finitude...
Grafting Seiberg-Witten monopoles.
Graphs with prescribed mean curvature on hyperbolic spaces.
Grassmannian structures on manifolds.
Gravitational scattering of electromagnetic field by Schwarzschild black-hole
Gromov's K-Area and Symplectic Rigidity.