Tuesday, September 25, 2012

1009.1435 (Holly Carley et al.)

Constructing graphs over $R^n$ with small prescribed mean-curvature    [PDF]

Holly Carley, Michael Kiessling
In this paper a convergent series expansion is constructed to solve the prescribed mean curvature equation for n-dimensional hypersurfaces in n+1 dimensional Euclidean or Minkowskian space(time) which are graphs of a smooth real function u, and whose mean curvature function H is not too large in Hoelder norm, and integrable. Our approach is inspired by the Maxwell-Born-Infeld theory of electromagnetism in Minkowski spacetime, for which our method yields the first systematic way of explicitly computing the electrostatic potential u for regular charge densities proportional to H and small Born parameter. Therefore, after the general n-dimensional problems have been treated with the help of nonlinear Hodge theory and Banach algebra estimates, our approach is reworked in more detail for n=3.
View original: http://arxiv.org/abs/1009.1435

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