Abstract
Let be a polygonal Jordan curve in . We show that if satisfies certain conditions, then the least-area Douglas-Radó disk in with boundary is unique and is a smooth graph. As our conditions on are not included amongst previously known conditions for embeddedness, we are enlarging the set of Jordan curves in which are known to be spanned by an embedded least-area disk. As an application, we consider the conjugate surface construction method for minimal surfaces. With our result we can apply this method to a wider range of complete catenoid-ended minimal surfaces in .
Citation
Wayne ROSSMAN. "On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces." J. Math. Soc. Japan 52 (1) 25 - 40, January, 2000. https://doi.org/10.2969/jmsj/05210025
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