Abstract
We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS.
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The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford University, where this paper was extensively rewritten, are gratefully acknowledged.
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Taylor, J.E. On the global structure of crystalline surfaces. Discrete Comput Geom 6, 225–262 (1991). https://doi.org/10.1007/BF02574687
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DOI: https://doi.org/10.1007/BF02574687