Minimal submanifolds with bounded second fundamental form.
Minimal surfaces and 3-manifolds of non-negative Ricci curvature.
Minimal surfaces and the affine Toda field model.
Minimal surfaces in a complex projective space whose mean curvature vectors are eigenvectors.
Minimal surfaces in foliated manifolds.
Minimal surfaces in pseudohermitian geometry
We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...
Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the case
We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces...
Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case
We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces...
Minimal surfaces, the Dirac operator and the Penrose inequality
Minimal surfaces via loop groups.
Minimal Surfaces with Isolated Singularities.
Minimal tensor product immersions.
Minimal tori in S4.
Minimal Varieties and Harmonic Maps in Tori.
Minimal varieties with trivial canonical classes, I.
Minimalflächen mit freiem Rand in Riemannschen Mannigfaltigkeiten.
Minimizing energy among homotopic maps.
Minimizing movements for dislocation dynamics with a mean curvature term
We prove existence of minimizing movements for the dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity solutions of the corresponding level-set equation. We also prove the consistency of this approach, by showing that any minimizing movement coincides with the smooth evolution...
Minimizing pseudo-harmonic maps in manifolds.
Minkowski versus Euclidean rank for products of metric spaces.