|
The Wills conjecture
Author(s):
Noah
Samuel
Brannen
Journal:
Trans. Amer. Math. Soc.
349
(1997),
3977-3987.
MSC (1991):
Primary 52A40
MathSciNet review:
1373630
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Two strengthenings of the Wills conjecture, an extension of Bonnesen's inradius inequality to  -dimensional space, are obtained. One is the sharpest of the known strengthenings of the conjecture in three dimensions; the other employs techniques which are fundamentally different from those utilized in the other proofs.
References:
- 1.
- A. D. Aleksandrov, On the theory of mixed volumes of convex bodies, Mat. Sb. 3 (1938), no. 45, 28-46. (Russian).
- 2.
- J. Bokowski, Eine verschärfte ungleichung zwischen Volumen, Oberfläche und Inkugelradius im
 , Elem. Math. 28 (1973), 43-44.MR 48:7119 - 3.
- J. Bokowski and E. Heil, Integral representations of quermassintegrals and bonnesen-style inequalities, Arch. Math. 47 (1986), 79-89.MR 88b:52008
- 4.
- G. Bol, Beweis einer Vermutung von H. Minkowski, Abh. Math. Sem. Univ. Hamburg 15 (1943), 37-56.MR 7:474f
- 5.
- T. Bonnesen, Les problèmes des isopérimetres et des isépiphanes, Gauthier-Villars, Paris, 1929.
- 6.
- G. D. Chakerian, Higher dimensional analogues of an isoperimetric inequality of Benson, Mathematische Nachrichten 48 (1971), 33-41. MR 44:4643
- 7.
- V. I. Diskant, A generalization of Bonnesen's inequalities, Soviet Math. Doklady 14 (1973), no. 6, 1728-1731 (translation of Doklady Akad. Nauk SSSR 213 (1973), 519-521). MR 49:3688
- 8.
- H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer, Berlin, 1957.MR 21:1561
- 9.
- G. Matheron, La formule de Steiner pour les érosions, Journal of Applied Probability 15 (1978), 126-135. MR 58:12874
- 10.
- R. Osserman, Bonnesen-style isoperimetric inequalities, American Math. Monthly 86 (1979), 1-29.MR 80h:52013
- 11.
- J. R. Sangwine-Yager, Bonnesen-style inequalities for Minkowski relative geometry, Transactions of the American Mathematical Society 307 (1988), no. 1, 373-382.MR 89g:52007
- 12.
- -, A Bonnesen-style inradius inequality in 3-space, Pacific Journal of Mathematics 134 (1988), 173-178.MR 89f:52032
- 13.
- R. Schneider, Convex bodies: The Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993.MR 94d:52007
- 14.
- B. Teissier, Bonnesen-type inequalities in algebraic geometry, Seminar on Differential Geometry (Princeton), Princeton University Press, 1982, pp. 85-105.MR 83d:52010
- 15.
- J. M. Wills, Zum Verhaltnis von Volumen zur Oberfläche bei konvexen Körpern, Arch. Math 21 (1970), 557-560.MR 43:3923
- 16.
- -, Minkowski's successive minima and the zeros of a convexity function, Monatsh. Math. 109 (1990), 157-164.MR 91f:52012
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
52A40
Retrieve articles in all Journals with
MSC (1991):
52A40
Additional Information:
Noah
Samuel
Brannen
Affiliation:
2-36-6 Tama-cho, Fuchu-shi, Tokyo 183, Japan
Email:
b-noah@hoffman.cc.sophia.ac.jp
DOI:
10.1090/S0002-9947-97-01716-9
PII:
S 0002-9947(97)01716-9
Keywords:
Circumradius,
convex body,
inner parallel body,
inradius,
mixed volume,
quermassintegral.
Received by editor(s):
February 9, 1995
Received by editor(s) in revised form:
August 15, 1995
Copyright of article:
Copyright
1997,
American Mathematical Society
|
