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Introduction à l’étude globale des tissus sur une surface holomorphe

Vincent Cavalier, Daniel Lehmann (2007)

Annales de l’institut Fourier

Beaucoup de concepts sur les tissus n’ont été étudiés que localement. Il apparaît que certains d’entre eux se laissent globaliser, mais pas toujours de façon immédiate. Le premier objectif de cet article est de préciser à chaque fois ce qu’il en est, et de mettre en place les outils utiles à une étude globale des tissus sur une surface holomorphe M arbitraire, et en particulier sur le plan projectif complexe ℙ 2 . Certains concepts nouveaux vont alors apparaître, tels le type (ou le degré si M = ℙ 2 ), la...

Introduction to mean curvature flow

Roberta Alessandroni (2008/2009)

Séminaire de théorie spectrale et géométrie

This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute the equation...

Invariance groups of relative normals

Thomas Binder, Martin Wiehe (2005)

Banach Center Publications

We investigate a two-parameter family of relative normals that contains Manhart's one-parameter family and the centroaffine normal. The invariance group of each of these normals is classified, and variational problems are studied. The results are Euler-Lagrange equations for the hypersurfaces that are critical with respect to the area functionals of the induced and semi-Riemannian volume forms and a classification of the critical hyperovaloids in the two-parameter family.

Invariance of g -natural metrics on linear frame bundles

Oldřich Kowalski, Masami Sekizawa (2008)

Archivum Mathematicum

In this paper we prove that each g -natural metric on a linear frame bundle L M over a Riemannian manifold ( M , g ) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define g -natural metrics on the orthonormal frame bundle O M and we prove the same invariance result as above for O M . Hence we see that, over a space ( M , g ) of constant sectional curvature, the bundle O M with an arbitrary g -natural metric G ˜ is locally homogeneous.

Invariance of global solutions of the Hamilton-Jacobi equation

Ezequiel Maderna (2002)

Bulletin de la Société Mathématique de France

We show that every global viscosity solution of the Hamilton-Jacobi equation associated with a convex and superlinear Hamiltonian on the cotangent bundle of a closed manifold is necessarily invariant under the identity component of the group of symmetries of the Hamiltonian (we prove that this group is a compact Lie group). In particular, every Lagrangian section invariant under the Hamiltonian flow is also invariant under this group.

Invariance properties of the Laplace operator

Eichhorn, Jürgen (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The paper deals with a special problem of gauge theory. In his previous paper [The invariance of Sobolev spaces over noncompact manifolds, Partial differential equations, Proc. Symp., Holzhaus/GDR 1988, Teubner- Texte Math. 112, 73-107 (1989; Zbl 0681.58011)], the author introduced the Sobolev completions 𝒞 ¯ P k of the space 𝒞 P of all G-connections on a G-principal fibre bundle P. In the present paper, under the assumption of bounded curvatures and their...

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