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- Title
INFINITE BOUNDARY VALUE PROBLEMS FOR CONSTANT MEAN CURVATURE GRAPHS IN H² x R AND S² x R.
- Authors
Hauswirth, Laurent; Rosenberg, Harold; Spruck, Joel
- Abstract
Abstract. We extend the classical exsitence and uniqueness theory of Jenkins-Serrin (H = 0) and Spruck (H > 0) for the constant mean curvature equation over a domain in R[sub2], to domains in H[sub2] or S[sub2]. This theory allows prescribed boundary data including plus or minus infinity on entire arcs of the boundary. Necessarily these arc must have curvature +2H or -2H with respect to the domain. We give necessary and sufficient conditions for existence in terms of so called admissible polygons. The key idea, as in previous proofs, is to study the "flux" of monotone increasing and decreasing sequences of solutions.
- Subjects
BOUNDARY value problems; CURVATURE; SURFACES of constant curvature; DIFFERENTIAL equations; BOUNDARY element methods
- Publication
American Journal of Mathematics, 2009, Vol 131, Issue 1, p195
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.0.0040