Osaka Journal of Mathematics

A variational problem related to conformal maps

Nobumitsu Nakauchi

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Abstract

In this paper we are concerned with a variational problem for a functional related to the conformality of maps between Riemannian manifolds. We give the first variation formula, the second variation formula, a kind of the monotonicity formula and a Bochner type formula. We also consider a variational problem of minimizing the functional in each 3-homotopy class of the Sobolev space.

Article information

Source
Osaka J. Math. Volume 48, Number 3 (2011), 719-741.

Dates
First available in Project Euclid: 26 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1317044944

Mathematical Reviews number (MathSciNet)
MR2837678

Zentralblatt MATH identifier
1230.53039

Subjects
Primary: 58E99: None of the above, but in this section 58E20: Harmonic maps [See also 53C43], etc. 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Citation

Nakauchi, Nobumitsu. A variational problem related to conformal maps. Osaka J. Math. 48 (2011), no. 3, 719--741. https://projecteuclid.org/euclid.ojm/1317044944.


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