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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 246, Pages 13–35 (Mi znsl547)  
Visibility curves for ovals

M. L. Egorov, V. A. Zalgaller

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (356 kB)
Abstract: For $C^1$-smooth strictly convex oval, the class of visibility curves is introduced. The equivalence of four definitions of this class of curves is proved, and the possible types of the shortest curves of visibility are studied. Several exstremal problems for the curve of visibility of the circle are solved.
Received: 14.03.1996
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 100, Issue 3, Pages 2194–2208
DOI: https://doi.org/10.1007/s10958-000-0005-5
Bibliographic databases:
UDC: 514.172.2
Language: Russian
Citation: M. L. Egorov, V. A. Zalgaller, “Visibility curves for ovals”, Geometry and topology. Part 2, Zap. Nauchn. Sem. POMI, 246, POMI, St. Petersburg, 1997, 13–35; J. Math. Sci. (New York), 100:3 (2000), 2194–2208
Citation in format AMSBIB
\Bibitem{EgoZal97}
\by M.~L.~Egorov, V.~A.~Zalgaller
\paper Visibility curves for ovals
\inbook Geometry and topology. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 246
\pages 13--35
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl547}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1631851}
\zmath{https://zbmath.org/?q=an:0928.52002}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 100
\issue 3
\pages 2194--2208
\crossref{https://doi.org/10.1007/s10958-000-0005-5}
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