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Rabinowitz Floer homology and symplectic homology

Kai Cieliebak, Urs Frauenfelder, Alexandru Oancea (2010)

Annales scientifiques de l'École Normale Supérieure

The first two authors have recently defined Rabinowitz Floer homology groups R F H * ( M , W ) associated to a separating exact embedding of a contact manifold ( M , ξ ) into a symplectic manifold ( W , ω ) . These depend only on the bounded component V of W ∖ M . We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V , which in turn maps to Rabinowitz Floer homology R F H * ( M , W ) , which then maps to symplectic cohomology of V . We compute R F H * ( S T * L , T * L ) , where S T * L is the unit cosphere bundle of a closed manifold...

Ramification of the Gauss map of complete minimal surfaces in ℝ 3 and ℝ 4 on annular ends

Gerd Dethloff, Pham Hoang Ha (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this article, we study the ramification of the Gauss map of complete minimal surfaces in ℝ 3 and ℝ 4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto ([4], [5]) and Ru ([13], [14]) for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a complete minimal surface cannot have more branching (and in particular not avoid more values) than on the whole complete minimal surface. We thus give an improvement...

Random lines and tessellations in a plane.

Luis A. Santaló (1980)

Stochastica

Our purpose is the study of the so called mixed random mosaics, formed by superposition of a given tesellation, not random, of congruent convex polygons and a homogeneous Poisson line process. We give the mean area, the mean perimeter and the mean number of sides of the polygons into which such mosaics divide the plane.

Rapport asymptotique de courbure, courbure positive et non effondrement

Alix Deruelle (2011/2012)

Séminaire de théorie spectrale et géométrie

On s’intéresse ici à un invariant géométrique associé à toute variété riemannienne non compacte : le rapport asymptotique de courbure. On étudie son influence sur la topologie de la variété sous-jacente en présence d’autres contraintes géométrico-topologiques portant sur le volume asymptotique, la positivité de la courbure (de Ricci) et/ou la finitude du groupe fondamental (à l’infini).

Rarita-Schwinger type operators on spheres and real projective space

Junxia Li, John Ryan, Carmen J. Vanegas (2012)

Archivum Mathematicum

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger...

Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga, M. Tezuka (1987)

Annales de l'institut Fourier

We show that an orientable fibration whose fiber has a homotopy type of homogeneous space G / U with rank G = rang U is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of G plays a key role in the proof. We also show that it is valid for mod. p coefficients if p does not divide the order of the Weyl group of G .

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