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The theory of surfaces is interpreted these days as a prototype of submanifold geometry and is characterized by the substantial application of PDE methods and methods from the theory of integrable systems, in addition to the more classical techniques from real and/or complex analysis. In addition, surfaces with singularities are studied intensively. In this workshop we brought together all the main strands of modern surface theory.
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Uwe Abresch, Josef Dorfmeister, Masaaki Umehara, Progress in Surface Theory. Oberwolfach Rep. 7 (2010), no. 2, pp. 1225–1318