Every point is critical |
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| Authors: | Imre Bá rá ny,Jin-ichi Itoh,Costin Vî lcu,Tudor Zamfirescu |
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| Affiliation: | 1. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary;2. Department of Mathematics, University College London, Gower Street, London WC1E6BT, England, United Kingdom;3. Faculty of Education, Kumamoto University, Kumamoto 860-8555, Japan;4. “Simion Stoilow” Institute of Mathematics of the Roumanian Academy, P.O. Box 1-764, Bucharest 014700, Romania;5. Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany;6. “Abdus Salam” School of Mathematical Sciences, GC University, Lahore, Pakistan |
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| Abstract: | We show that, for any compact Alexandrov surface S (without boundary) and any point y in S, there exists a point x in S for which y is a critical point. Moreover, we prove that uniqueness characterizes the surfaces homeomorphic to the sphere among smooth orientable surfaces. |
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| Keywords: | 53C45 53C22 |
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