Sobolev maps on manifolds: degree, approximation, lifting

Coincidence Classes in Nonorientable Manifolds

In this article we studied Nielsen coincidence theory for maps between manifolds of same dimension without hypotheses on orientation. We use the definition of semi-index of a class, we review the definition of defective classes and study the appearance of defective root classes. We proof a semi-index product formula type for lifting maps and we presented conditions such that defective coinciden...

Strong density results in trace spaces of maps between manifolds

We deal with strong density results of smooth maps between two manifolds X and Y in the fractional spaces given by the traces of Sobolev maps in W .

Sobolev maps into the projective line with bounded total variation

Variational problems for Sobolev maps with bounded total variation that take values into the 1-dimensional projective space are studied. We focus on the different features from the case of Sobolev maps with bounded conformal p-energy that take values into the p-dimensional projective space, for p ≥ 2 integer, recently studied in [18]. In the last decades there has been a growing interest in the...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

On the Degree of Approximation by Manifolds of Finite Pseudo-Dimension

The pseudo-dimension of a real-valued function class is an extension of the VC dimension for set-indicator function classes. A classH of finite pseudo-dimension possesses a useful statistical smoothness property. In [10] we introduced a nonlinear approximation width ρn(F , Lq ) = infHn dist(F ,Hn, Lq ) which measures the worstcase approximation error over all functions f ∈ F by the best manifol...