caa a22 4500 605496552 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10231-014-0429-z doi (NATIONALLICENCE)springer-10.1007/s10231-014-0429-z Proper holomorphic maps in harmonic map theory [Elektronische Daten] [Elisabetta Barletta, Sorin Dragomir] We determine all proper holomorphic maps of balls $${\mathbb {B}}_2 \rightarrow {\mathbb {B}}_3$$ B 2 → B 3 admitting a $$C^3$$ C 3 extension up to the boundary of $${\mathbb {B}}_2$$ B 2 and whose boundary values $$S^3 \rightarrow S^5$$ S 3 → S 5 are subelliptic harmonic maps (in the sense of Jost and Xu in Trans Am Math Soc 350(11):4633-4649,1998). A new numerical CR invariant, the CR degree of a CR map of spheres $$S^{2n+1} \rightarrow S^{2N+1}$$ S 2 n + 1 → S 2 N + 1 , is introduced and used to distinguish among the spherical equivalence classes in Faran's list $$P^*(2,3)$$ P ∗ ( 2 , 3 ) (cf. Faran in Invent Math 68:441-475,1982). As an application, the boundary values $$\phi $$ ϕ of Alexander's map $$\Phi \in P(2,3)$$ Φ ∈ P ( 2 , 3 ) (cf. Alexander in Indiana Univ Math J 26:137-146,1977) is shown to be homotopically nontrivial, as a map of $$\{ (z,w) \in S^3 : w + \overline{w} > 0 \}$$ { ( z , w ) ∈ S 3 : w + w ¯ > 0 } into $$S^5 {\setminus } S^3$$ S 5 \ S 3 . Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Proper holomorphic map nationallicence Subelliptic harmonic map nationallicence CR degree nationallicence Barletta Elisabetta Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, 85100, Potenza, Italy aut Dragomir Sorin Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, 85100, Potenza, Italy aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1469-1498 0373-3114 194:5<1469 2015 194 10231 https://doi.org/10.1007/s10231-014-0429-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0429-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barletta Elisabetta Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, 85100, Potenza, Italy aut NATIONALLICENCE 700 1- Dragomir Sorin Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell'Ateneo Lucano 10, 85100, Potenza, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1469-1498 0373-3114 194:5<1469 2015 194 10231