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A compact minimal shadow boundary in Euclidean space is totally geodesic |
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| Authors: | Antonio J Di Scala Jesus Jerónimo-Castro Gabriel Ruiz-Hernández |
| Institution: | 1. Dipartimento Di Matematica, Politecnico Di Torino, Turin, Italy 2. Facultad de Ingenieria, UAQ, Santiago de Quer??taro, QRO, Mexico 3. Instituto de Matem??ticas, UNAM, Mexico City, Mexico |
| Abstract: | We prove that a compact minimal shadow boundary of a hypersurface in Euclidean space is totally geodesic. We show that shadow boundaries detect principal directions and umbilical points of a hypersurface. As application we deduce that every shadow boundary of a compact strictly convex surface contains at least two principal directions. |
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