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.
|Title of host publication||Differential Geometry of Submanifolds : Proceedings of RIMS Symposium|
|Publication status||Published - 2012|
|Event||RIMS Symposium : Differential Geometry of Submanifolds - |
Duration: 27 Jun 2011 → 29 Jun 2011
|Conference||RIMS Symposium : Differential Geometry of Submanifolds|
|Period||27/06/2011 → 29/06/2011|
Brander, D. (2012). Geometric Cauchy problems for spacelike and timelike CMC surfaces in R2,1. In Differential Geometry of Submanifolds: Proceedings of RIMS Symposium (pp. 85-93). Kyoto University. RIMS Kokyuroku, Vol.. 1775