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Harmonic maps in singular geometry and rigidity
Georgios Daskalopoulos, Chikako Mese
This survey reviews results on harmonic maps into spaces of non-positive curvature, with a focus on targets that lack smooth structure. More precisely, we consider targets that are…
Best Lipschitz maps and Earthquakes
Georgios Daskalopoulos, Karen Uhlenbeck
This is the third paper in a series in which we prove Thurston's conjectural duality between best Lipschitz maps and transverse measures. In the second paper we found a special cla…
Notes on Harmonic Maps
Georgios Daskalopoulos, Chikako Mese
This is set of notes prepared for the Summer School on non-Abelian Hodge theory in Abbaye de Saint-Jacut de la Mer June, 6-19, 2022. We cover the following topics: Lecture 1. Harmo…
Infinite energy harmonic maps from Riemann surfaces to CAT(0) spaces
Georgios Daskalopoulos, Chikako Mese
We present some results about harmonic maps with possibly infinite energy from punctured Riemann surfaces to CAT(0) spaces. In particular, we give precise estimates of their energy…
Analytic properties of Stretch maps and geodesic laminations
Georgios Daskalopoulos, Karen Uhlenbeck
In a 1998 preprint, Bill Thurston outlined a Teichmuller theory for hyperbolic surfaces based on maps between surfaces which minimize the Lipschitz constant (minimum stretch or bes…
Infinite energy maps and rigidity
Georgios Daskalopoulos, Chikako Mese
We extend Siu's and Sampson's celebrated rigidity results to non-compact domains. More precisely, let be a smooth quasi-projective variety with universal cover and l…
Uniqueness of equivariant harmonic maps to symmetric spaces and buildings
Georgios Daskalopoulos, Chikako Mese
We prove uniqueness of equivariant harmonic maps into irreducible symmetric spaces of non-compact type and Euclidean buildings associated to isometric actions by Zariski dense subg…
Transverse Measures and Best Lipschitz and Least Gradient Maps
Georgios Daskalopoulos, Karen Uhlenbeck
We exhibit the duality between best Lipschitz (infinity harmonic) maps and least gradient maps in the case of maps from surfaces to the circle. We show that given a homotopy class…
Rigidity of Teichmuller Space
Georgios Daskalopoulos, Chikako Mese
We prove the holomorphic rigidity conjecture of Teichmüller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichmüller space…
Classification of Weil-Petersson Isometries
Georgios Daskalopoulos, Richard Wentworth
This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmueller space for any choice of pseudo-Anosov mapping class. As a…