New PDF release: A la recherche de la topologie perdue: I Du côté de chez

By Lucien Guillou, Alexis Marin

ISBN-10: 0817633294

ISBN-13: 9780817633295

Show description

Read or Download A la recherche de la topologie perdue: I Du côté de chez Rohlin, II Le côté de Casson PDF

Similar geometry and topology books

Download e-book for iPad: Discrete Differential Geometry by Alexander I. Bobenko (auth.), Alexander I. Bobenko, John M.

Discrete differential geometry is an energetic mathematical terrain the place differential geometry and discrete geometry meet and engage. It offers discrete equivalents of the geometric notions and techniques of differential geometry, corresponding to notions of curvature and integrability for polyhedral surfaces.

Extra resources for A la recherche de la topologie perdue: I Du côté de chez Rohlin, II Le côté de Casson

Sample text

Let u1 ≤ u2 be two solutions of our free boundary problem in B1 , with F (u2 ) Lipschitz and 0 ∈ F (u2 ). Assume that in B1−ε vε (x) = sup u1 ≤ u2 (x) Bε (x) that for b > 0, small, vε (x0 ) ≤ (1 − bε)u2 (x0 ) x0 = 34 en and that B1/8 (x0 ) ⊂ Ω+ (u1 ) .

4) that is, if τ (σ) is the unit vector in the direction σ − c0 σ, ν en , Dτ (σ) u ≥ 0 . We show that the family {τ (σ); σ ∈ Γ(θ, en )} contains a new cone of directions Γ(θ1 , ν1 ), strictly larger than Γ(θ, en ). 4) implies that the gain in the opening is measured by the quantity E(σ) = c0 σ, ν , |σ| = 1, σ ∈ Γ(θ, en ). This implies that for a small μ > 0, for any vector σ ∈ ∂Γ(θ, en ) there exist a ball Bρ(σ) (σ) where ρ(σ) = |σ|μ σ, ν = |σ|μ sin(E(σ)) π E(σ) = − α(σ, ν) , 2 such that the directional derivative of u is nonnegative along any vector in Bρ(σ) (σ).

We show that the family {τ (σ); σ ∈ Γ(θ, en )} contains a new cone of directions Γ(θ1 , ν1 ), strictly larger than Γ(θ, en ). 4) implies that the gain in the opening is measured by the quantity E(σ) = c0 σ, ν , |σ| = 1, σ ∈ Γ(θ, en ). This implies that for a small μ > 0, for any vector σ ∈ ∂Γ(θ, en ) there exist a ball Bρ(σ) (σ) where ρ(σ) = |σ|μ σ, ν = |σ|μ sin(E(σ)) π E(σ) = − α(σ, ν) , 2 such that the directional derivative of u is nonnegative along any vector in Bρ(σ) (σ). The envelope of the balls Bρ(σ) (σ) contains a cone Γ(θ1 , ν1 ) that contains Γ(θ, en ) and with an opening θ1 > θ.

Download PDF sample

A la recherche de la topologie perdue: I Du côté de chez Rohlin, II Le côté de Casson by Lucien Guillou, Alexis Marin


by Brian
4.4

Rated 4.70 of 5 – based on 48 votes