If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding ...If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.展开更多
The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bod...The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.展开更多
基金Supported by the National Natural Science Foundation of China(10801140)Chongqing Research Program of Basic Research and Frontier Technology(2013-JCYJ-A00005)the Foundation of Chongqing Normal University(13XLZ05)
文摘If L is a star body in Rn whose central（n-i）-slices have the same（n-i）-dimensional measure μn-1（with appropriate density） as the central（n-i）-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn（K）≤μn（L）. This extends a generalized Funk＇s section theorem for volumes to that for measures.
文摘The Funk＇s section theorem in the n-complex space Cn is investigated. It turns out that this theorem does not admit an extension for the class of general origin-symmetric star bodies in Cn but for a class of star bodies called generalized complex intersection bodies. A quasi-version of Funk＇s section theorem in Cn is established then.
