Calculus of Variations and Geometric Evolution Problems: by Fabrice Bethuel, Gerhard Huisken, Stefan Müller, Klaus

By Fabrice Bethuel, Gerhard Huisken, Stefan Müller, Klaus Steffen (auth.), Stefan Hildebrandt, Michael Struwe (eds.)

The foreign summer season institution on Calculus of adaptations and Geometric Evolution difficulties used to be held at Cetraro, Italy, 1996. The contributions to this quantity replicate relatively heavily the lectures given at Cetraro that have supplied a picture of a reasonably large box in research the place lately we've seen many very important contributions. one of the subject matters taken care of within the classes have been variational tools for Ginzburg-Landau equations, variational versions for microstructure and part transitions, a variational remedy of the Plateau challenge for surfaces of prescribed suggest curvature in Riemannian manifolds - either from the classical perspective and within the surroundings of geometric degree theory.

Show description

Read Online or Download Calculus of Variations and Geometric Evolution Problems: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 15–22, 1996 PDF

Best calculus books

A history of vector analysis : the evolution of the idea of a vectorial system

Concise and readable, this article levels from definition of vectors and dialogue of algebraic operations on vectors to the idea that of tensor and algebraic operations on tensors. It also includes a scientific learn of the differential and vital calculus of vector and tensor services of house and time.

Real and Abstract Analysis: A modern treatment of the theory of functions of a real variable

This booklet is firstly designed as a textual content for the path frequently referred to as "theory of services of a true variable". This path is at this time cus­ tomarily provided as a primary or moment yr graduate direction in usa universities, even supposing there are indicators that this type of research will quickly penetrate top department undergraduate curricula.

Volume doubling measures and heat kernel estimates on self-similar sets

This paper reviews the next 3 difficulties: while does a degree on a self-similar set have the amount doubling estate with appreciate to a given distance? Is there any distance on a self-similar set below which the contraction mappings have the prescribed values of contractions ratios? And whilst does a warmth kernel on a self-similar set linked to a self-similar Dirichlet shape fulfill the Li-Yau style sub-Gaussian diagonal estimate?

Additional info for Calculus of Variations and Geometric Evolution Problems: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 15–22, 1996

Sample text

REFERENCES [A] L. Almeida, Thesis. [AB1] L. Ahneida and F. Bethuel, Multiplicity results for the Ginzburg-Landau equation in presence of symmetries, to appear in Houston J. of Math. [AB2] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equation, preprint. [BBH] F. Bethuel, H. Brezis and F. Hdlein, Ginzburg-Landau vortices, Birkha/iser, (1994). [BBH2] F. Bethuel, H. Brezis and F. H61ein, Asymptotics for the minimization of a Ginzburg-Landau functional, CMc. Var. and PDE, 1, (1993) 123-148.

1) is a nonlinear parabolic system of second order. Although there are some similarities to the harmonic map heatflow, this deformation law is more nonlinear in nature since the leading second order operator depends on the geometry of the solution at each time rather than the initial geometry. There is a very direct interplay between geometric properties of the underlying manifold (N"+l,~) and the geometry of tile evolving hypersurface which leads to applications both in differential geometry and mathematical physics.

More generally, the elementary symmetric functions - f = S,~, 1 < m _< n, satisfy -(Of/O)~i) > 0 on the convex cone F,,, = {)~ E lR'*lSl(A ) > 0, 1 < l < m}, yielding shorttime existence for corresponding initial data. 1) on Fk. In particular, this yields a shorttime existence result for the harmonic mean curvature flow on convex initial data, since - f = [t = S,,/S,,-t. iv) The inverse mean curvature flow with f = H -~ satisfies -(0f/0,k~) = H -2, yielding shorttime existence of a classical smooth solution for any initial data of positive mean curvature.

Download PDF sample

Rated 4.02 of 5 – based on 39 votes