Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications

Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro

doi:10.1090/S0002-9939-99-04892-3

Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications
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by Wayne Rossman, Masaaki Umehara and Kotaro Yamada PDF

Proc. Amer. Math. Soc. 127 (1999), 2147-2154 Request permission

Abstract:

Using the Bryant representation, we define a flux on homology classes of CMC-$1$ surfaces in $\mathcal {H}^3$, satisfying a balancing formula which is useful to show nonexistence of certain kinds of complete CMC-$1$ surfaces.

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