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By Mark Mandelkern

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34 37 37 38 39 40 42 44 46 47 49 51 53 54 54 57 59 63 63 63 66 69 69 72 74 77 77 78 81 83 85 85 34 Georgios D. Daskalopoulos and Richard A. 2 Properness of the energy . . . . . . 3 Convexity of energy and length functionals . 4 Further applications . . . . . . . . 5 Harmonic maps to Teichmüller space . . .

34 37 37 38 39 40 42 44 46 47 49 51 53 54 54 57 59 63 63 63 66 69 69 72 74 77 77 78 81 83 85 85 34 Georgios D. Daskalopoulos and Richard A. 2 Properness of the energy . . . . . . 3 Convexity of energy and length functionals . 4 Further applications . . . . . . . . 5 Harmonic maps to Teichmüller space . . . . . . 1 Existence of equivariant harmonic maps . . . . 1 Maps to the completion .

2 Superrigidity . . . . . . . . . . . 2 Harmonic maps from singular domains . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 87 88 90 90 90 92 93 95 95 96 99 1 Introduction Teichmüller theory is rich in applications to topology and physics. By way of the mapping class group the subject is closely related to knot theory and three-manifolds.

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