No abstract

In this paper, we prove a sharp anisotropic L p Minkowski inequality involving the total L p anisotropic mean curvature and the anisotropic p-capacity, for any bounded domains with smooth boundary in R n . As consequences, we obtain an anisotropic Willmore inequality, a sharp anisotropic Minkowski inequality for outward F -minimising sets and a sharp volumetric anisotropic Minkowski inequality. For the proof, we utilize a nonlinear potential theoretic approach which has been recently developed in [2].

No abstract

The equivariant CR minimal immersions from the round 3-sphere S 3 into the complex projective space CP n have been classified by the third author explicitly (J London Math Soc 68: 223-240, 2003). In this paper, by employing the equivariant condition which implies that the induced metric is left-invariant, and that all geometric properties of S 3 = SU(2) endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra su(2), we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere S 3 into CP n without the assumption of constant sectional curvatures.

We prove an integral inequality for compact orientable real hypersurfaces of the complex quadric Q n (n ≥ 3) in terms of their shape operator S and Reeb vector field ξ. As direct consequences, we obtain new characterizations for real hypersurfaces of Q n with isometric Reeb flow. Such hypersurfaces have been classified by J. Berndt and Y.