[1]
|
Zvavitch, A. (2005) The Busemann-Petty Problem for Arbitrary Measures. Mathematische
Annalen, 331, 867-887. https://doi.org/10.1007/s00208-004-0611-5
|
[2]
|
Koldobsky, A. (2000) A Functional Analytic Approach to Intersection Bodies. Geometric and
Functional Analysis, 10, 1507-1526. https://doi.org/10.1007/PL00001659
|
[3]
|
Koldobsky, A. and Zvavitch, A. (2015) An Isomorphic Version of the Busemann-Petty Problem
for Arbitrary Measures. Geometriae Dedicata, 174, 261-277.
https://doi.org/10.1007/s10711-014-0016-x
|
[4]
|
Zymonopoulou, M. (2008) The Complex Busemann-Petty Problem for Arbitrary Measures.
Archiv der Mathematik, 91, 436-449. https://doi.org/10.1007/s00013-008-2863-x
|
[5]
|
Rubin, B. and Zhang, G. (2004) Generalizations of the Busemann-Petty Problem for Sections
of Convex Bodies. Journal of Functional Analysis, 213, 473-501.
https://doi.org/10.1016/j.jfa.2003.10.008
|
[6]
|
Rubin, B. (2006) The Lower Dimensional Busemann-Petty Problem with Weights. Mathemati-
ka, 53, 235-245. https://doi.org/10.1112/S0025579300000115
|
[7]
|
Zhang, G. (1996) Sections of Convex Bodies. American Journal of Mathematics, 118, 319-340.
https://doi.org/10.1353/ajm.1996.0021
|
[8]
|
Bourgain, J. and Zhang, G. (1998) On a Generalization of the Busemann-Petty Problem.
In: Ball, K. and Milman, V., Eds., Convex Geometric Analysis, MSRI Publications, Vol. 34,
Cambridge University Press, New York, 65-76.
|
[9]
|
Koldobsky, A. (2000) A Functional Analytic Approach to Intersection Bodies. Geometric and
Functional Analysis, 10, 1507-1526. https://doi.org/10.1007/PL00001659
|
[10]
|
Milman, E. (2005) Generalized Intersection Bodies. Journal of Functional Analysis, 240, 530-
567. https://doi.org/10.1016/j.jfa.2006.04.004
|
[11]
|
Busemann, H. and Petty, C.H. (1956) Problems on Convex Bodies. Mathematica Scandinavica,
4, 88-94. https://doi.org/10.7146/math.scand.a-10457
|
[12]
|
Ball, K. (1988) Some Remarks on the Geometry of Convex Sets. In: Lindenstrauss, J. and
Milman, V., Eds., Geometric Aspects of Functional Analysis 1986-1987, Lecture Notes in
Mathematics, Vol. 1317, Springer, Berlin, 224-231. https://doi.org/10.1007/BFb0081743
|
[13]
|
Barthe, F., Fradelizi, M. and Maurey, B. (1999) A Short Solution to the Busemann-Petty
Problem. Positivity, 3, 95-100. https://doi.org/10.1023/A:1009777119957
|
[14]
|
Bourgain, J. (1991) On the Busemann-Petty Problem for Perturbations of the Ball. Geometric
and Functional Analysis, 1, 1-13. https://doi.org/10.1007/BF01895416
|
[15]
|
Gardner, R.J. (1994) A Positive Answer to the Busemann-Petty Problem in Three Dimensions.
Annals of Mathematics, 140, 435-447. https://doi.org/10.2307/2118606
|
[16]
|
Gardner, R.J., Koldobsky, A. and Schlumprecht, T. (1999) An Analytic Solution to the
Busemann-Petty Problem on Sections of Convex Bodies. Annals of Mathematics, 149, 691-703.
https://doi.org/10.2307/120978
|
[17]
|
Giannopoulos, A. (1990) A Note on a Problem of H. Busemann and C.M. Petty Concerning
Sections of Symmetric Convex Bodies. Mathematika, 37, 239-244.
https://doi.org/10.1112/S002557930001295X
|
[18]
|
Larman, D.G. and Rogers, C.A. (1975) The Existence of a Centrally Symmetric Convex Body
with Central Cross-Sections That Are Unexpectedly Small. Mathematika, 22, 164-175.
https://doi.org/10.1112/S0025579300006033
|
[19]
|
Lutwak, E. (1988) Intersection Bodies and Dual Mixed Volumes. Advances in Mathematics,
71, 232-261. https://doi.org/10.1016/0001-8708(88)90077-1
|
[20]
|
Papadimitrakis, M. (1992) On the Busemann-Petty Problem about Convex, Centrally Sym-
metric Bodies in Rn. Mathematika, 39, 258-266. https://doi.org/10.1112/S0025579300014996
|
[21]
|
Zhang, G. (1994) Centered Bodies and Dual Mixed Volumes. Transactions of the AMS, 345,
777-801. https://doi.org/10.1090/S0002-9947-1994-1254193-9
|
[22]
|
Zhang, G. (1999) A Positive Answer to the Busemann-Petty Problem in R4. Annals of Math-
ematics, 149, 535-543. https://doi.org/10.2307/120974
|
[23]
|
Giannopoulos, A. and Koldobsky, A. (2016) Variants of the Busemann-Petty Problem and of
the Shephard Problem. arXiv:1601.02231
|
[24]
|
Koldobsky, A. and Yaskin, V. (2008) The Interface between Convex Geometry and Harmonic
Analysis. In: CBMS Regional Conference Series in Mathematics, Vol. 108, American Mathe-
matical Society, Providence, RI. https://doi.org/10.1090/cbms/108
|
[25]
|
Rubin, B. (2008) Intersection Bodies and Generalized Cosine Transforms. Advances in Math-
ematics, 218, 696-727. https://doi.org/10.1016/j.aim.2008.01.011
|
[26]
|
Yaskin, V. (2006) A Solution to the Lower Dimensional Busemann-Petty Problem in the Hyper-
bolic Space. Journal of Geometric Analysis, 16, 735-745. https://doi.org/10.1007/BF02922139
|
[27]
|
Zymonopoulou, M. (2008) The Complex Busemann-Petty Problem for Arbitrary Measures.
Archiv der Mathematik, 91, 436-449. https://doi.org/10.1007/s00013-008-2863-x
|
[28]
|
Grinberg, E. and Zhang, G. (1999) Convolutions, Transforms and Convex Bodies. Proceedings
of the London Mathematical Society, 78, 77-115. https://doi.org/10.1112/S0024611599001653
|
[29]
|
Helgason, S. (1984) Groups and Geometric Analysis. Academic Press, Cambridge MA.
|
[30]
|
Helgason, S. (1999) The Radon Transform. 2nd Edition, Birkhauser, Boston.
https://doi.org/10.1007/978-1-4757-1463-0
|
[31]
|
Rubin, B. (2002) Inversion Formulas for the Spherical Radon Transform and the Generalized
Cosine Transform. Advances in Applied Mathematics, 29, 471-497.
https://doi.org/10.1016/S0196-8858(02)00028-3
|