Bonnesen-style inequalities and pseudo-perimeters for polygons

Journal of Geometry

Volumn 60, Issue 1-2, 1997, Pages 188-201

  Zhang, Xin Min ^a  

^a UNIVERSITY OF SOUTH ALABAMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009090199     PISSN: 00472468     EISSN: 14208997     Source Type: Journal    
DOI: 10.1007/BF01252226     Document Type: Article

References (23)

1. CHEVEL, I.: Eigenvalues in Riemannian Geometry, Academic Press, New York, 1984.
2. CHEVEL, I.: Riemannian Geometry: A Modern Introduction, Cambridge Press, New York, 1993.
3. FEJES TÓTH, L.: Lagerungen in der Ebene, auf der Kugel und im Raum, Die Grundlehren der math. Wissenschaften, vol. 65, Springe-Verlag (1972).
4. CHRIS FISHER, J., RUOFF, D. and SHILLETO, J.: Perpendicular Polygons, Amer. Math. Monthly, Jan. (1985)23-37.
5. GROEMER, H.: Stability Properties of Geometric Inequalities, Amer. Math. Monthly, 97(1990)382-394.
6. GROEMER, H.: Stability Theorems for Convex Domains of Constant Width, Canad. Math. Bull. 31(1988)328-337.
7. GRUBER, P. M. and WILLS, J. M.: Handbook of Convex Geometry, North-Holland, 1993.
8. HARDY, G., LITTLEWOOD, J. E. and POLYA, G.: Inequalities, Cambridge Univ. Press, Cambridge, New York, 1951.
9. KAZARINOFF, M. D.: Geometric Inequalities, New Math. Library, Math. Assoc. of America, 1961.
10. KU, H. T., KU, M. C. and ZHANG, X. M.: Analytic and Geometric Isopermetric Inequalities, Journal of Geometry, vol.53(1995)100-121.
11. KU, H. T., KU, M. C. and ZHANG, X. M.: Isoperimetric Inequalities on Surfaces of Constant Curvature, (Preprint).
12. MACNAB, D. S.: Cyclic Polygons and Related Questions, Math. Gazette, 65(1981)22-28.
13. MARSDEN, J. E. and TROMBA, A. J.: Vector Calculus, Second Edition, W. H. Freeman and Company, 1981.
14. MITRINOVIĆ, D. S.: Analytic Inequalities, Springer-Verlag Berlin-Heidelberg-New York, 1970.
15. OSSERMAN, R.: The Isoperimetric Inequality, Bull. Amer. Math. Soc. 84(1978), 1182-1238.
16. OSSERMAN, R.: Bonnesen-style Isoperimetric Inequalities, Amer. Math. Monthly, No.1(1979)1-29.
17. PERI, W. and ZUCCO: On Blaschke's Extension of Bonnnesen's Inequality, Geometria Dedicata, vol.48, No.3(1993)349.
18. POLYA, G. and SZEGO, G.: Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, No.27, Princeton Univ., Princeton, 1951.
19. ROBBINS, DAVID P.: Area of Polygons Inscribed in a Circle, Amer. Math. Monthly, [June-July] (1995)523-530.
20. SANGWINE-YAGER, J. R.: Bonnesen-style Inequalities for Minkowski Relative Geometry, Trans. AMS., vol.307(1988)373-382.
21. TANG, D.: Discrete Wirtinger and Isoperimetric Type Inequalities, Bull. Austral. Math. Soc. 43(1991),467-474.
22. TEISSIER, B.: Bonnesen-type Inequalities in Algebraic Geometry, Seminar on Differential Geometry, Edited by S.T.Yau, Princeton Univ. Press and Univ. of ToKyo press, Princeton, 1982.
23. ZHANG, X. M.: A Refinement of the Discrete Wirtinger Inequality, Journal of Mathematical Analysis and Applications, to appear.