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Quadratic tilt-excess decay and strong maximum principle for varifolds

Reiner Schätzle (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper, we prove that integral n -varifolds μ in codimension 1 with H μ L loc p ( μ ) , p > n , p 2 have quadratic tilt-excess decay tiltex μ ( x , ϱ , T x μ ) = O x ( ϱ 2 ) for μ -almost all x , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature H μ , unless the smooth manifold is locally contained in the support of μ .

Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Georgi Ganchev, Velichka Milousheva (2014)

Open Mathematics

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.

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