设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒...设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C2芬斯勒度量。Let F1 and F2 be two Finsler metrics on smooth manifold M1 and M2,respectively.The conformally doubly warped product Finsler metric F2=e2σ(f22F12+f12F22) is a Finsler metric endowed on the M=M1×M2 ,where f1、f2 and σ are positive smooth functions on M1 、M2 and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C2-like Finsler metric.展开更多
An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of c...An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.展开更多
Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a genera...Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.展开更多
文摘设F1和F2分别是光滑流形M1和M2上的芬斯勒度量,共形双扭曲积芬斯勒度量是在乘积流形M=M1×M2上赋予的芬斯勒度量F2=e2σ(f22F12+f12F22), 其中f1、f2和 σ分别是M1 、M2和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C2芬斯勒度量。Let F1 and F2 be two Finsler metrics on smooth manifold M1 and M2,respectively.The conformally doubly warped product Finsler metric F2=e2σ(f22F12+f12F22) is a Finsler metric endowed on the M=M1×M2 ,where f1、f2 and σ are positive smooth functions on M1 、M2 and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C2-like Finsler metric.
基金supported by the NSFC(12171378)supported by the Characteristic innovation projects of universities in Guangdong province(2023K-TSCX381)+3 种基金supported by the Young Top-Talent program of Chongqing(CQYC2021059145)the Major Special Project of NSFC(12141101)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937).
文摘An upper estimate of the new curvature entropy is provided,via the integral inequality of a concave function.For two origin-symmetric convex bodies in R^(n),this bound is sharper than the log-Minkowski inequality of curvature entropy.As its application,a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
基金supported by the Postgraduate Scientic Research Innovation Project of Chongqing Normal University(YKC24010)Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China(12141101)+2 种基金the Young Top-Talent program of Chongqing(CQYC2021059145)the Technology Research Foundation of Chongqing Educational committee(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937)。
文摘Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.
