In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fu...In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.展开更多
In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well a...In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well as some pinching theorems on＇the second fundamental form.展开更多
In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.
In this note,we consider the mappings h:X→Y between doubly connected Riemann surfaces having leastρ-Dirichlet energy.For a pair of doubly connected Riemann surfaces,in which X has finite conformal modulus,we establi...In this note,we consider the mappings h:X→Y between doubly connected Riemann surfaces having leastρ-Dirichlet energy.For a pair of doubly connected Riemann surfaces,in which X has finite conformal modulus,we establish the following principle:A mapping h in the class H2(X,Y)of strong limits of homeomorphisms in Sobolev space W1,2(X,Y)isρ-energy-minimal if and only if its Hopf-differential is analytic in X and real along?X.It improves and extends the result of Iwaniec et al.(see Theorem 1.4 in[Arch.Ration.Mech.Anal.,209,401–453(2013)]).Furthermore,we give an application of the principle.Anyρ-energy minimal diffeomorphism isρ-harmonic,however,we give a 1/|w|~2-harmonic diffemorphism which is not 1/|w|~2-energy minimal diffeomorphism.At last,we investigate the necessary and sufficient conditions for the existence of 1/|w|~2-harmonic mapping from doubly connected domainΩto the circular annulus A(1,R).展开更多
文摘In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.
基金Foundation item： Supported by the National Natural Science Foundation of China（ll071005） Supported by the Natural Science Foundation of Anhui Province Education Department（KJ2008A05zC）
文摘In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons＇ type inte- gral inequality of compact submanifoids as well as some pinching theorems on＇the second fundamental form.
基金Natural Science Foundation of Education Department of Anhui Province （No. 2004kj166zd）.
文摘In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.
基金Supported by the National Natural Science Foundation of China(Grant No.11701459)the Natural Science Foundation of Sichuan Provincial Department of Education(Grant No.17ZB0431)+1 种基金the Research Startup of China West Normal University(Grant No.17E88)supported by the Science and Technology Development Fund of Tianjin Commission for Higher Education(Grant No.2017KJ095)。
文摘In this note,we consider the mappings h:X→Y between doubly connected Riemann surfaces having leastρ-Dirichlet energy.For a pair of doubly connected Riemann surfaces,in which X has finite conformal modulus,we establish the following principle:A mapping h in the class H2(X,Y)of strong limits of homeomorphisms in Sobolev space W1,2(X,Y)isρ-energy-minimal if and only if its Hopf-differential is analytic in X and real along?X.It improves and extends the result of Iwaniec et al.(see Theorem 1.4 in[Arch.Ration.Mech.Anal.,209,401–453(2013)]).Furthermore,we give an application of the principle.Anyρ-energy minimal diffeomorphism isρ-harmonic,however,we give a 1/|w|~2-harmonic diffemorphism which is not 1/|w|~2-energy minimal diffeomorphism.At last,we investigate the necessary and sufficient conditions for the existence of 1/|w|~2-harmonic mapping from doubly connected domainΩto the circular annulus A(1,R).
