The Björling problem for non-minimal constant mean curvature surfaces

Details The Björling problem for non-minimal constant mean curvature surfaces The Björling problem for non-minimal constant mean curvature surfaces

2009-08-23

arxiv.org/abs/0908.3274v2

Comm. Anal. Geom. 18 (2010) 171-194

Mathematics

Differential Geometry

18 Pages, 16 figures. Typographical corrections in version 2

Scientific paper

The classical Bj\"orling problem is to find the minimal surface containing a given real analytic curve with tangent planes prescribed along the curve. We consider the generalization of this problem to non-minimal constant mean curvature (CMC) surfaces, and show that it can be solved via the loop group formulation for such surfaces. The main result gives a way to compute the holomorphic potential for the solution directly from the Bj\"orling data, using only elementary differentiation, integration and holomorphic extensions of real analytic functions. Combined with an Iwasawa decomposition of the loop group, this gives the solution, in analogue to Schwarz's formula for the minimal case. Some preliminary examples of applications to the construction of CMC surfaces with special properties are given.

Affiliated with

Also associated with

No associations

Rating

The Björling problem for non-minimal constant mean curvature surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Björling problem for non-minimal constant mean curvature surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Björling problem for non-minimal constant mean curvature surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-363683