Minimal volume of slabs in the complex cube
Authors:
Hermann König and Alexander Koldobsky
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1709-1717
MSC (2010):
Primary 46B20, 52A20, 52A40; Secondary 46B04, 52A21
Posted:
September 6, 2011
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Abstract: We study the volume of sections and slabs in the
References
Bibliography
[B] Keith
Ball , Cube slicing in
𝑅ⁿ Proc. Amer. Math. Soc.
97 (1986), no. 3 ,
465–473. MR
840631 (87g:60018) , http://dx.doi.org/10.1090/S0002-9939-1986-0840631-0
[BK] F.
Barthe and A.
Koldobsky , Extremal slabs in the cube and the Laplace
transform , Adv. Math. 174 (2003), no. 1,
89–114. MR
1959893 (2004f:52004) , http://dx.doi.org/10.1016/S0001-8708(02)00055-5
[Ha] H.
Hadwiger , Gitterperiodische Punktmengen und Isoperimetrie ,
Monatsh. Math. 76 (1972), 410–418 (German). MR 0324550
(48 #2902)
[He] Douglas
Hensley , Slicing the cube in 𝑅ⁿ
and probability (bounds for the measure of a central cube slice in
𝑅ⁿ by probability methods) Proc. Amer. Math. Soc. 73 (1979), no. 1 , 95–100. MR 512066
(80b:60025) , http://dx.doi.org/10.1090/S0002-9939-1979-0512066-8
[OP] Krzysztof
Oleszkiewicz and Aleksander
Pełczyński , Polydisc slicing in
𝐶ⁿ , Studia Math. 142 (2000),
no. 3, 281–294. MR 1792611
(2001f:52014)
[P] Georg
Polya , Berechnung eines bestimmten Integrals , Math. Ann.
74 (1913), no. 2, 204–212 (German). MR
1511759 , http://dx.doi.org/10.1007/BF01456040
[V] Jeffrey
D. Vaaler , A geometric inequality with applications to linear
forms , Pacific J. Math. 83 (1979), no. 2,
543–553. MR
557952 (81d:52007)
[W] G.
N. Watson , A treatise on the theory of Bessel functions ,
Cambridge Mathematical Library, Cambridge University Press, Cambridge,
1995. Reprint of the second (1944) edition. MR 1349110
(96i:33010)
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Additional Information
Hermann König
Affiliation:
Mathematisches Seminar, Universität zu Kiel, 24098 Kiel, Germany
Email:
hkoenig@math.uni-kiel.de
Alexander Koldobsky
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email:
koldobsk@math.missouri.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11019-0
PII:
S 0002-9939(2011)11019-0
Received by editor(s):
August 26, 2010
Received by editor(s) in revised form:
January 21, 2011
Posted:
September 6, 2011
Additional Notes:
The first author was partially supported by the American Institute of MathematicsCommunicated by:
Thomas Schlumprecht
Article copyright:
© Copyright 2011 American Mathematical Society
-dimensional cube for complex scalars. In particular, we investigate the directions of minimal volume for a small width of the slab. 