Document Type

Article

Date

11-1-2009

Embargo Period

11-11-2011

Disciplines

Mathematics

Description/Abstract

The conjecture in question concerns the existence of a harmonic homeomorphism between circular annuli A(r,R) and A(r*,R*), and is motivated in part by the existence problem for doubly-connected minimal surfaces with prescribed boundary. In 1962 J.C.C. Nitsche observed that the image annulus cannot be too thin, but it can be arbitrarily thick (even a punctured disk). Then he conjectured that for such a mapping to exist we must have the following inequality, now known as the Nitsche bound: R*/r* is greater than or equal to (R/r+r/R)/2. In this paper we give an affirmative answer to his conjecture. As a corollary, we find that among all minimal graphs over given annulus the upper slab of catenoid has the greatest conformal modulus.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0908.1253

Source

Harvested from arXiv.org

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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