Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting han...Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting handled by Gage.展开更多
This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f...This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.展开更多
文摘Using Picard's theorem and the Leray-Schauder fixed point theorem to reinvestigate the area-preserving convex curve flow in the plane which is considered as a coupled system and thus different from the setting handled by Gage.
基金in part supported by NSERC of Canada and the Finnish Cultural Foundation
文摘This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.
