About the isoperimetric property of λ-convex lunes on the Lobachevsky plane

Authors

  • K.D. Drach

DOI:

https://doi.org/10.15407/dopovidi2014.11.011

Keywords:

Lobachevsky plane, λ-convex curve

Abstract

We give a sharp lower bound of the area of a domain that can be enclosed by a closed embedded λ-convex curve of a given length on the Lobachevsky plane.

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References

Burago Yu. D., Zalgaller V. A. Geometric inequalities, Leningrad: Nauka, 1980 (in Russian).

Borisenko A. A., Drach K. D. Matem. zametki, 2014, 95, Iss. 5: 656–665 (in Russian).

Borisenko A. A., Drach K. D. J. Dynam. and Control Syst., 2015, 21, Iss. 3: 311-327. https://doi.org/10.1007/s10883-014-9221-z

Borisenko A. A., Drach K. D. Mat. sb., 2013, 204, No 11: 21–40 (in Russian).

Howard R., Treibergs A. Rocky Mountain J. Math., 1995, 25, No 2: 635–684. https://doi.org/10.1216/rmjm/1181072242

Milka A. D. Ukr. geok. sb. 1978, 21: 88–91 (in Russian).

Milyutin A. A., Dmitruk A. V., Osmolovsky N. P. The maximum principle in optimal control, Moscow: Izd-vo TSPI pri mekh.-mat. fakultete MGU, 2004 (in Russian).

Fillmore J. P. Proc. Amer. Math. Soc., 1970, 24: 705–709.

Bliashke V. Circle and ball, Moscow: Nauka, 1967 (in Russian).

Kelley H. J., Kopp R. E., Moyer H. G. Singular extremals. In: Topics in Optimization / Ed. G. Leitmann, New York: Academ. Press, 1967: 63–103. https://doi.org/10.1016/s0076-5392(09)60039-4

Published

11.03.2025

How to Cite

Drach, K. (2025). About the isoperimetric property of λ-convex lunes on the Lobachevsky plane . Reports of the National Academy of Sciences of Ukraine, (11), 11–15. https://doi.org/10.15407/dopovidi2014.11.011