Abstract
We prove uncountably many new analytic and geometric isoperimetric inequalities associated with the solutions of second order ordinary differential equations.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
BHALLA, G. S.: Brahmaguta's quadrilateral, Math. Comput. Ed. 20 (1986), No. 3, 191–196.
DO CARMO, P.: Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976.
CHEVEL J.: Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984.
HARDY, G., LITTLEWOOD, J. E. and POLYA G.: Inequalities, Cambridge Univ. Press, Cambridge, New York, 1951.
GILLETT, P.: Calculus and Analytic Geometry, D. C. Heath and Company, 1981.
KAC, M.: Can you hear the shape of a drum? Amer. Math. Monthly 73 (1966),1–23.
KAZARINOFF, M. D.: Geometric Inequalities, New Math. Library, Math. Assoc. of America, 1961.
MACNAB, D. S.: Cyclic polygons and related questions, Math. Gazette 65 (1981), 22–28.
MARSDEN, J. E. and TROMBA, A. J.: Vector Calculus, Second Edition, W. H. Freeman and Company, 1981.
OSSERMAN, R.: The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182–1238.
POLYA, G. and SZEG, G.Ö, Isoperimetric Inequalities in Mathematical Physics, Ann. of Math., Studies No. 27, Princeton Univ. Princeton, 1951.
SCHEON, R. and YAU, S. T.: Differential Geometry, Beijing, China, 1988.
SU, B.: Lectures on Differential Geometry, World Scientific, Singapore, 1980.
TANG D.: Discrete Wirtinger and isoperimetric type inequalities, Bull. Austral. Math. Soc. 43 (1991), 467–474.
YAGLON, I. M.: A Simple Non-Euclidean Geometry and Its Physical Basis. Springer-Verlag, New York, Heidelberg and Berlin, 1979.