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)
Variational problem of some quadratic functionals in complex analysis. (English) Zbl 0945.30023
For maps between marked closed Riemann surfaces a program of H. E. Rauch (see {\it M. Gerstenhaber} and {\it H. E. Rauch}, Proc. Natl. Acad. Sci. 40, 808-812, 991-994 (1954; Zbl 0056.07502) studied the existence of Teichmüller’s extremal map by minimizing the energy functionals. The paper under review contributes to that program, by examining related quadratic functionals of maps.

MSC:
30C70Extremal problems for conformal and quasiconformal mappings, variational methods
30F45Conformal metrics (hyperbolic, Poincaré, distance functions)
30F60Teichmüller theory
WorldCat.org
Full Text: DOI
References:
[1] Ahlfors, L. V.: On quasiconformal mappings. J. d’anal. Math. 4, 1-54 (1954) · Zbl 0057.06506
[2] Courant, R.: Dirichlet’s principle, conformal mapping, and minimal surfaces. (1950) · Zbl 0040.34603
[3] Eells, J.; Lemaire, L.: Another report on harmonic maps. Bull. London math. Soc. 20, 385-524 (1988) · Zbl 0669.58009
[4] Gerstenhaber, M.; Rauch, H. E.: On extremal quasiconformal mappings I. Proc. nat. Acad. sci. USA 40, 808-812 (1954) · Zbl 0056.07502
[5] Grötzsch, H.: Über möglichst konforme abbildungen von schlichten bereichen. Ber. verh. Sachs akad. Wiss. Leipzig math.-nat. Kl. 84, 114-120 (1932)
[6] Jost, J.; Schoen, R.: On the existence of harmonic diffeomorphisms between surfaces. Invent. math. 66, 353-359 (1982) · Zbl 0488.58009
[7] Morse, M.: The topology of pseudo-harmonic functions. Duke math. J. 13, 21-42 (1947)
[8] Morse, M.; Heins, M.: Topological methods in the theory of functions of a single complex variable. Ann. math. 46, 600-666 (1945) · Zbl 0063.04118
[9] Nitsche, J. C. C.: Vorlesungen über minimalflächen. (1975) · Zbl 0319.53003
[10] Ozawa, M.: On grötzsch’s affine mapping. Kōdai math. Seminar rep. 8, 112-114 (1956) · Zbl 0073.06903
[11] Schwartz, L.: Théorie des distributions. (1950) · Zbl 0037.07301
[12] Teichmüller, O.: Extremale quasikonforme abbildungen und quadratische differentiale. Abh. preuss. Akad. wiss. Math.-nat. Kl. jahrgang 1939 22, 1-197 (1940)
[13] Tôki, Y.: A topological characterization of pseudo-harmonic functions. Osaka math. J. 3, 101-122 (1951) · Zbl 0042.33503
[14] Väisälä, J.: Lectures onn. Lecture notes in mathematics 229 (1971)
[15] Weinstock, R.: Calculus of variations. (1952) · Zbl 0049.19503