Phases of unimodular complex valued maps: optimal estimates, the factorization method, and the sum-intersection property of Sobolev spaces

— Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an ex- ceptional low dimensional phenomenon.. This

In any domain, existence of critical points (Berlyand-Rybalko 2010, Dos Santos 2009, Berlyand-M.-Rybalko-Sandier 2014, Lamy-M. 2014). In thin domains, existence of

∗ In multiply connected domains, critical points do exist for small ε (Berlyad, Rybalko 10 for doubly connected domain, Dos Santos 09 for general multiply connected domains).. ∗

In Section 5.1, we give presentations of certain braid groups of T 2 , in Section 5.2, we describe the set of homotopy classes of split 2-valued maps of T 2 , and in Section 5.3,

In [22], we showed that spheres and real and complex projective spaces of even dimen- sion have the fixed point property for n-valued maps, and we expressed the problem of deforming

Structure of the paper In the following section, we apply known results to obtain estimates of the energy of optimal partitions in the case of a disk, a square or an

Distances between classes of sphere-valued Sobolev maps Haim Brezis, Petru Mironescu, Itai Shafrir.. To cite

The Zipf’s law for short Chinese texts behaves much similar to those for short English texts, but for long texts, the rank-frequency relations of Chinese characters are quite