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Another proof for the rigidity of Clifford minimal hypersurfaces of [S.sup.n]
(2011-10-13)
Let M [subset] [S.sup.n] be a minimal hypersurface, and let us denote by A the shape operator of M. In this paper we give an alternative proof of the theorem that states that if [[absolute value of A].sup.2] = n - 1, then ...
The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms
(SPRINGER, 2011)
LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, ...
Immersions of finite geometric type in Euclidean spaces
(Kluwer Academic PublDordrechtHolanda, 2002)
Hipersuperfícies conformemente euclidianas com curvatura média ou escalar constante
(Universidade Federal de São CarlosUFSCarPrograma de Pós-Graduação em Matemática - PPGMCâmpus São Carlos, 2016-11-10)
In this work we study conformally flat hypersurfaces f: M3 ^ Q4(c) with three distinct principal curvatures in a space form with constant sectional curvature c, under the assumption that either its mean curvature H or its ...
Interface dynamics in semilinear wave equations
(Springer, 2020)
We consider the wave equation epsilon(2)(-partial derivative(2)(t) + Delta)u + f(u) = 0 for 0 < epsilon << 1, where f is the derivative of a balanced, double-well potential, the model case being f(u) = u - u(3). For equations ...
A lower bound for the norm of the second fundamental form of minimal hypersurfaces of Sn+1
(2003)
The aim of this paper is to give an estimate for the squared norm S of the second fundamental form A of a compact minimal hypersurface Mn⊂Sn+1 in terms of the gap n−λ1 , where λ1 stands for the first eigenvalue of the ...