Isothermal Coordinates On Surfaces
Gauss (1822) proved the existence of isothermal coordinates on an arbitrary surface with a real analytic metric, following results of Lagrange (1779) on surfaces of revolution. Results for Hölder continuous metrics were obtained by Korn (1916) and Lichtenstein (1916). Later accounts were given by Morrey (1938), Ahlfors (1955), Bers (1952) and Chern (1955). A particularly simple account using the Hodge star operator is given in DeTurck & Kazdan (1981).
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