On the solution of reverse Dido’s Problem for convex surfaces of revolution
DOI:
https://doi.org/10.15407/dopovidi2016.04.007Keywords:
normal curvature, Pontryagin’s maximum principle, reverse isoperimetric inequality, λ-convexityAbstract
By applying Pontryagin’s maximum principle, we prove a reverse isoperimetric inequality and thus solve a reverse Dido’s Problem for λ-convex surfaces of revolution in the three-dimensional Euclidean space.
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Burago Yu. D., Zalgaller V. A. Geometric inequalities, Leningrad: Nauka, 1980 (in Russian).
Howard R., Treibergs A. Rocky Mountain J. Math., 1995, 25, No 2: 635–684. https://doi.org/10.1216/rmjm/1181072242
Gard A. C. Reverse Isoperimetric Inequalities in R3
: PhD Thesis, Columbus: Ohio State University, 2012.
Borisenko A., Drach K. Math. Notes, 2014, 95, No 5: 590–598 (in Russian). https://doi.org/10.1134/S0001434614050034
Drach K. D. Dopov. Nac. akad. nauk Ukr., 2014, No 11: 11–15 (in Russian; English version: arXiv:1402.2688 [math.DG]).
Borisenko A., Drach K. J. Dyn. Control Syst., 2015, 21, No 3: 311–327. https://doi.org/10.1007/s10883-014-9221-z
van Heijenoort J. Comm. Pure Appl. Math., 1952, 5: 223–242. https://doi.org/10.1002/cpa.3160050302
Blaschke W. Kreis und Kugel, Moskva: Nauka, 1967 (in Russian).
Borisenko A. A., Drach K. D. Dopov. Nac. akad. nauk Ukr., 2015, No 3: 11–16 (in Russian; English version: arXiv: 1402.2691[math.DG]).
Milyutin A. A., Dmitruk A. V., Osmolovskij N. P. Maximum principle in optimal control, Moscow: Izd. CPI pri mekh.-mat. fakul’tete MGU, 2004 (in Russian).
Kelley H. J., Kopp R. E., Moyer H. G. Topics in Optimization, Ed. G. Leitmann, New York: Academic Press, 1967: 63–103.
Borisenko A., Drach K. Sb. Math., 2013, 204, No 11: 1565–1583. https://doi.org/10.1070/SM2013v204n11ABEH004349
Borisenko A. Diff. Geom. Appl., 2002, 17: 111–121. https://doi.org/10.1016/S0926-2245(02)00102-X
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