Comparison principles for hypersurfaces of prescribed mean curvature.
Comparison results between minimal barriers and viscosity solutions for geometric evolutions
Complete minimal hypersurfaces in hyperbolic n-manifolds.
Complete minimal hypersurfaces with prescribed asymptotics at infinity.
Complete Minimal Varieties in Hyperbolic Space.
Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior
In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
Complete nonorientable minmal surfaces in R3.
Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a -valued function defined on the boundary of a bounded regular domain of . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...
Concentrated monotone measures with non-unique tangential behavior in
We show that for every there is a set such that is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and has the -dimensional density between and everywhere in the support.
Conformal mapping and inverse conductivity problem with one measurement
This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...
Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
Conformally invariant variational integrals and the removability of isolated singularities.
Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.
Connected components of sets of finite perimeter and applications to image processing
This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called -connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite...
Connecting topological Hopf singularities
Smooth maps between riemannian manifolds are often not strongly dense in Sobolev classes of finite energy maps, and an energy drop in a limiting sequence of smooth maps often is accompanied by the production (or bubbling) of an associated rectifiable current. For finite 2-energy maps from the 3 ball to the 2 sphere, this phenomenon has been well-studied in works of Bethuel-Brezis-Coron and Giaquinta-Modica-Soucek where a finite mass 1 dimensional rectifiable current occurs whose boundary is the...
Connectivity properties of the range of a weak diffeomorphism
Construction de surfaces à courbure moyenne constante
Contact shape optimization based on the reciprocal variational formulation
The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out....
Continuity, curvature, and the general covariance of optimal transportation
Continuity of Minimal Surfaces with Piecewise Smooth Free Boundaries.