We discuss recent work of the author and collaborators on generalizations of Björling’s classical problem to the case of constant non-zero mean curvature surfaces in 2+1-dimensional spacetime. The aim is to give an overview, and to point out the similarities and differences between the two cases of timelike and spacelike surfaces. Applications to the construction of CMC surfaces with prescribed singularities are also described.
数理解析研究所講究録: Proceedings of Rims Symposium, 2012, p. 85-93
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RIMS Symposium : Differential Geometry of Submanifolds, 2012