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Surfaces with parallel mean curvature in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$
Surfaces with parallel mean curvature math
2010/11/24
We consider surfaces with parallel mean curvature vector (pmc surfaces) in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$, and, more generally, in cosymplectic space forms. We in...
Flows of constant mean curvature tori in the 3-sphere: The equivariant case
curvature tori the 3-sphere
2010/11/18
We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the m...
Generalized $1$-harmonic Equation and The Inverse Mean Curvature Flow
Generalized $1$-harmonic Equation The Inverse Mean Curvature Flow
2010/11/19
We introduce and study generalized $1$-harmonic equations (1.1). Using some ideas and techniques in studying $1$-harmonic functions from [W1] (2007), and in studying nonhomogeneous $1$-harmonic funct...
Existence of translating solutions to the flow by powers of mean curvature on unbounded domains
Dirichlet problem mean curvature flow elliptic equation unbounded domain.
2010/12/7
In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain in Rn(n ≥ 2). T...
Horizontal Connection and Horizontal Mean Curvature in Carnot Groups
Carnot groups Nonholonomic connection Horizontal mean curvature Sub-Riemannian minimal surfaces
2007/12/13
In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli--Garofalo--Nhieu and Pauls who recently introduced sub-Riemannian minima...