In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an exi...In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an existence theorem of this kind of surfaces with prescribed principal curvatures. At last, we present two examples involving the rotation surfaces as the special case, and present several figures to the second example.展开更多
In this paper,we consider λ-translating solitons in R^(3).These surfaces are critical points of the weighted area when the density is a coordinate function.If λ=0,these surfaces evolve by translations along the mean...In this paper,we consider λ-translating solitons in R^(3).These surfaces are critical points of the weighted area when the density is a coordinate function.If λ=0,these surfaces evolve by translations along the mean curvature fow.We give a full classifcation ofλ-translating solitons that satisfy a linear Weingarten relation between their curvatures.These surfaces are planes,circular cylinders,grim reapers and certain types of cylindrical surfaces.We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.展开更多
In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
基金Supported by the SDFDP (Grant No.20050141011)the MATH+X Project Offiered by Dalian University of Technology (Grant No.MXDUT073005)
文摘In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an existence theorem of this kind of surfaces with prescribed principal curvatures. At last, we present two examples involving the rotation surfaces as the special case, and present several figures to the second example.
基金Supported by LiaoNing Revitalization Talents Program(Grant No.XLYC2203194)the key Project for Department of Liaoning Education(Grant No.LJ112410173072)+1 种基金partially supported by MINECO/MICINN/FEDER(Grant No.PID2023-150727NB-I00)by the"María de Maeztu"Excellence Unit IMAG,reference CEX2020-001105-M,funded by MCINN/AEI/10.13039/501100011033/CEX2020-001105-M。
文摘In this paper,we consider λ-translating solitons in R^(3).These surfaces are critical points of the weighted area when the density is a coordinate function.If λ=0,these surfaces evolve by translations along the mean curvature fow.We give a full classifcation ofλ-translating solitons that satisfy a linear Weingarten relation between their curvatures.These surfaces are planes,circular cylinders,grim reapers and certain types of cylindrical surfaces.We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.
基金Supported by the Joint Research of National Nature Science Foundation of ChinaNational Research Foundation(Grant No.11071032)Chern Institute of Mathematics and Northeastern University
文摘In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
