An improved uniqueness result for the harmonic map flow in two dimensions

Rupflin, Melanie
November 2008
Calculus of Variations & Partial Differential Equations;Nov2008, Vol. 33 Issue 3, p329
Academic Journal
Generalizing a result of Freire regarding the uniqueness of the harmonic map flow from surfaces to an arbitrary closed target manifold N, we show uniqueness of weak solutions u ? H 1 under the assumption that any upwards jumps of the energy function are smaller than a geometrical constant $$\epsilon^\star=\epsilon^\star(N)$$ , thus establishing a conjecture of Topping, under the sole additional condition that the variation of the energy is locally finite.


Related Articles

  • New Classes of Salagean type Meromorphic Harmonic Functions. Bostanci, Hakan; �zt�rk, Metin // International Journal of Mathematics Sciences;Winter2008, Vol. 2 Issue 1, p52 

    In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + ? using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for...

  • Subclasses of Multivalent Harmonic Mappings Defined by Convolution. SUBRAMANIAN, K. G.; STEPHEN, B. ADOLF; LEE, S. K. // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 3, p717 

    A new subclass of multivalent harmonic functions defined by convolution is introduced in this paper. The subclass generates known subclasses of multivalent harmonic functions, and thus provides a unified treatment in the study of these subclasses. Sufficient coefficient conditions are obtained...

  • UNIVALENT HARMONIC MAPPINGS INTO TWO-SLIT DOMAINS. Ganczar, Andrzej; Widomski, Jarosław // Journal of the Australian Mathematical Society;Feb2010, Vol. 88 Issue 1, p61 

    We study some classes of planar harmonic mappings produced with the shear construction devised by Clunie and Sheil-Small in 1984. The first section reviews the basic concepts and describes the shear construction. The main body of the paper deals with the geometry of the classes constructed.

  • Area Comparison, Superharmonic Functions, and Applications. Yang, Yi Hu // Acta Mathematica Sinica;2001, Vol. 17 Issue 2, p207 

    Abstract In this paper, we study some geometrical and analytic properties of manifolds with nonnegative sectional curvature at infinity. Then, we apply these results to the study of harmonic maps. Keywords Area comparison, Superharmonic functions, Harmonic maps

  • LANDAU’S THEOREM AND MARDEN CONSTANT FOR HARMONIC ν-BLOCH MAPPINGS. CHEN, SH.; PONNUSAMY, S.; WANG, X. // Bulletin of the Australian Mathematical Society;Aug2011, Vol. 84 Issue 1, p19 

    Our main aim is to investigate the properties of harmonic ν-Bloch mappings. Firstly, we establish coefficient estimates and a Landau theorem for harmonic ν-Bloch mappings, which are generalizations of the corresponding results in Bonk et al. [‘Distortion theorems for Bloch...

  • Some generalization of coefficient condition for complex harmonic mappings. Aldweby, Huda A.; Darus, Maslina // AIP Conference Proceedings;Apr2013, Vol. 1522 Issue 1, p930 

    Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk Δ can be written in the form [formula], where h and g are analytic in Δ several mathematicians examined classes of complex harmonic functions in the unit disk with some coefficient conditions....

  • Classifications of some special infinity-harmonic maps. Ze-Ping Wang; Ye-Lin Ou // Balkan Journal of Geometry & Its Applications;2009, Vol. 14 Issue 1, p120 

    ∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞-harmonic maps from and into a sphere, quadratic...

  • Properties of the Mappings That Are Close to the Harmonic Mappings. II. Kopylov, A. P. // Siberian Mathematical Journal;Jul/Aug2004, Vol. 45 Issue 4, p628 

    We continue studying the mappings that are close to the harmonic mappings (s-quasiharmonic mappings with s small). IF study originates with the previous articles of the author. The results of the article include a theorem on connection between the notion of s-quasiharmonic mapping and the...

  • GENERALIZED WARPED PRODUCT MANIFOLDS AND BIHARMONIC MAPS. DJAA, N. E. H.; BOULAL, A.; ZAGANE, A. // Acta Mathematica Universitatis Comenianae;2012, Vol. 81 Issue 2, p283 

    In this paper, we present some new properties for biharmonic and conformal biharmonic maps between generalized warped product manifolds.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics