Universität zu Köln

Vu, Duc-Viet (2020). EQUILIBRIUM MEASURES OF MEROMORPHIC SELF-MAPS ON NON-KAHLER MANIFOLDS. Trans. Am. Math. Soc., 373 (3). S. 2229 - 2251. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6850

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Abstract

Let X be a compact complex non-Kahler manifold and let f be a dominant meromorphic self-map of X. Examples of such maps are self-maps of Hopf manifolds, Calabi-Eckmann manifolds, non-tori nilmanifolds, and their blowups. We prove that if f has a dominant topological degree, then f possesses an equilibrium measure mu satisfying well-known properties as in the Kahler case. The key ingredients are the notion of weakly d.s.h. functions substituting d.s.h. functions in the Kahler case and the use of suitable test functions in Sobolev spaces. A large enough class of holomorphic self-maps with a dominant topological degree on Hopf manifolds is also given.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Vu, Duc-Viet UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-343091
DOI:	10.1090/tran/7994
Journal or Publication Title:	Trans. Am. Math. Soc.
Volume:	373
Number:	3
Page Range:	S. 2229 - 2251
Date:	2020
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6850
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TOPOLOGICAL-ENTROPY; ERGODIC PROPERTIES; RATIONAL MAPPINGS; CURRENTS; TRANSFORMATIONS; REGULARIZATION; THEOREM Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/34309