zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Harmonic diffeomorphisms between Riemannian manifolds. (English) Zbl 0738.58015
Variational methods, Proc. Conf., Paris/Fr. 1988, Prog. Nonlinear Differ. Equ. Appl. 4, 309-318 (1990).

[For the entire collection see Zbl 0713.00009.]

In this lecture I will speak principally about a joint work with J.- M. Coron [Compos. Math. 69, No. 2, 175-228 (1989; Zbl 0686.58012)] in which we studied the following problem: let M and N be two Riemannian manifolds with or without boundary, which are diffeomorphic, and let u be a harmonic C 1 -diffeomorphism between M and N. In the case where M and N have nonempty boundaries, we assume that the restriction of u to M is a diffeomorphism between M and N. Then we want to know if u is or is not a minimizing harmonic map, i.e. if u minimizes the energy functional among the maps which have the same boundary data as u and which are homotopic to u. In the case where M and N have empty boundaries, the answer is generally no because of the counterexample of the identity map from S 3 to S 3 : this is a harmonic diffeomorphism but the infimum of the energy in its homotopy class is zero [see J. Eells and J. H. Sampson, Am. J. Math. 86, 109-160 (1964; Zbl 0122.401)].

MSC:
58E20Harmonic maps between infinite-dimensional spaces
53C20Global Riemannian geometry, including pinching
35J50Systems of elliptic equations, variational methods