F-harmonic Maps as Global Maxima

ON f -BI-HARMONIC MAPS BETWEEN RIEMANNIAN MANIFOLDS

A. Both bi-harmonic map and f -harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study f -bi-harmonic maps as the critical points of the f -bi-energy functional 1 2 ∫ M f |τ(φ)| dvg. This class of maps generalizes both concepts of harmonic maps and biharmonic maps. We first derive the f -biharmonic map ...

Harmonic Mappings of Spheres

Introduction and statement of results. This announcement describes an elementary method of constructing harmonic maps in some cases not covered by the general existence theory. Recall that given smooth Riemannian manifolds N and M, with N compact, then the energy functional E:H(N,M) -> R is defined on a suitable manifold of maps H(iV, M ) and is given by E{ f ) = \ \n \df | . A map ƒ is said to...

Rigidity of harmonic measure

Let J be the Julia set of a conformal dynamics f . Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

On the Integrality of the Taylor Coefficients of Mirror Maps

Abstract. We show that the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(z)F(z) are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at z = 0. We also address the question of finding the largest integer u such that the Taylor coefficients of (zq(z)) are still integers. As consequences, we are...