We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variationa...We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871061)
文摘We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.
