Volume preserving flows for convex curves and surfaces in the hyperbolic space

doi:10.1016/j.jfa.2022.109685

CSpace

	Volume preserving flows for convex curves and surfaces in the hyperbolic space
	Wei, Yong 1; Yang, Bo 2
	2022-12-01
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	283 期号:11 页码:28
摘要	In this paper, we study the curvature flows of convex curves and surfaces in the hyperbolic space. In the first part, we consider the area preserving and length preserving is alpha-type curvature flows of smooth closed convex curves in the hy-perbolic plane H-2 and show that these two types of flows evolve convex curve to a geodesic circle exponentially in C-infinity topology. In the second part, we study the volume preserving Gauss curvature flow of smooth closed convex surfaces in H-3 and show that the solution remains convex and converges to a geodesic sphere exponentially in C-infinity topology. (C) 2022 Elsevier Inc. All rights reserved.
关键词	Curvature flow Hyperbolic space Curve Surface
DOI	10.1016/j.jfa.2022.109685
收录类别	SCI
语种	英语
资助项目	National Key R and D Program of China[2021YFA1001800] ; National Key R and D Program of China[2020YFA0713100] ; National Key R and D Program of China[KY0010000052] ; Uni-versity of Science and Technology of China
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000858842000001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60921
专题	中国科学院数学与系统科学研究院
通讯作者	Wei, Yong
作者单位	1.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China 2.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wei, Yong,Yang, Bo. Volume preserving flows for convex curves and surfaces in the hyperbolic space[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2022,283(11):28.
APA	Wei, Yong,&Yang, Bo.(2022).Volume preserving flows for convex curves and surfaces in the hyperbolic space.JOURNAL OF FUNCTIONAL ANALYSIS,283(11),28.
MLA	Wei, Yong,et al."Volume preserving flows for convex curves and surfaces in the hyperbolic space".JOURNAL OF FUNCTIONAL ANALYSIS 283.11(2022):28.