Publications

Preprints

2017:

• (with I. Prause) Quasiconformal extensions, Loewner chains, and the $\lambda$-Lemma, 14 pp. ArXiv:1712.08632

Papers accepted for publication

2018:

• (with D. Prokhorov) Value regions of univalent self-maps with two boundary fixed points, 12 pp. To appear in Ann. Acad. Sci. Fenn., Math. 43 (2018) ArXiv:1703.05835

•  Parametric representations and boundary fixed points of univalent self-maps of the unit disk, 18 pp. Accepted for publication in Proceedings of the INdAM Conference "Geometric Function Theory in Higher Dimension", Cortona (AR), ITALY, September 5-9, 2016. Springer INdAM Series. Vol. 26 ArXiv:1702.00344

Published papers

2017:

•  Parametric representation of univalent functions with boundary regular fixed points. Constr. Approx. 46 (2017), 435-458. Published online in April 2017 - DOI 10.1007/s00365-017-9376-4. ArXiv:1603.04043

• (with I. Hotta) Chordal Loewner chains with quasiconformal extensions. Math. Z. 285 (2017), No.3, 1063-1089. Published online in September 2016 - DOI 10.1007/s00209-016-1738-2. Full text is available here. ArXiv:1511.08077

2016:

• (with L. Arosio) Valiron and Abel equations for holomorphic self-maps of the polydisc. Internat. J. Math. 27 (2016), No.4 1650034 (16 pages). Published online in April 2016 - DOI 10.1142/S0129167X16500348. ArXiv:1509.04169

• (with F. Bracci) Contact points and fractional singularities for semigroups of holomorphic self-maps in the unit disc. J. Anal. Math. 130 (2016), No.1, 185-217. Published online in November 2016 - DOI 10.1007/s11854-016-0034-8. ArXiv:1309.2813.

• (with A. del Monaco) Chordal Loewner Equation, in Complex Analysis and Dynamical Systems VI. Part 2. Contemp. Math. 667 (2016) 63-77. ArXiv:1302.0898

2015:

• (with M. D. Contreras and S. Díaz-Madrigal) Slope Problem for Trajectories of Holomorphic Semigroups in the Unit Disk. Comput. Methods Funct. Theory 15 (2015) No.1, 117-124. Published online in September 2014 - DOI 10.1007/s40315-014-0092-9. ArXiv:1406.3614

• (with F. Bracci, M. D. Contreras and S. Díaz-Madrigal) Boundary regular fixed points in Loewner Theory. Ann. Mat. Pura Appl. 194 (2015) No.1, 221-245. Published online in August 2013 - DOI 10.1007/s10231-013-0372-4. ArXiv:1303.5216

2014:

•  Angular and unrestricted limits of one-parameter semigroups in the unit disk. J. Math. Anal. Appl. 417 (2014) No.1, 200-224. Published online in March 2014 - DOI 10.1016/j.jmaa.2014.02.057. ArXiv:1211.3965

• (with M. D. Contreras and S. Díaz-Madrigal) Local duality in Loewner equations. J. Nonlinear Convex Anal. 15 (2014) No.2, 269-297. ISRN IML-R- -16-11/12- -SE+fall

2013:

• (with M. D. Contreras and S. Díaz-Madrigal) Loewner Theory in annulus I: evolution families and differential equations. Trans. Amer. Math. Soc. 365 (2013) 2505-2543. Published online in November 2012 - DOI 10.1090/S0002-9947-2012-05718-7. ArXiv: 1011.4253v1

2011:

• (with M. D. Contreras and S. Díaz-Madrigal) Loewner Theory in annulus II: Loewner chains. Analysis and Mathematical Physics 1 (2011) No.4, 351-385. Published online in November 2011 - DOI 10.1007/s13324-011-0016-z. ArXiv:1105.3187v1

2010:

• (with M. D. Contreras and S. Díaz-Madrigal) Geometry behind chordal Loewner chains. Complex Analysis and Operator Theory 4 (2010) 541-587. Published online in March 2010 - DOI 10.1007/s11785-010-0057-6. ArXiv:1002.0826v1. ERRATUM.

• (with M. D. Contreras and S. Díaz-Madrigal) Loewner chains in the unit disk. Revista Matemática Iberoamericana 26 (2010) 975-1012. ArXiv:0902.3116v1

2009:

• (with E. Grong and A.Vasil'ev) Matching univalent functions and conformal welding. Ann. Acad. Sci. Fenn., Math. 34 (2009) 303-314. ArXiv:0806.0930v1

•  Carathéodory Convergence of Immediate Basins of Attraction to a Siegel Disk. Analysis and Mathematical Physics. Trends in Mathematics, 165-184. Birkhäuser Verlag Basel/Switzerland, 2009. DOI 10.1007/978-3-7643-9906-1_9. CHAPTER.

2005:

•  Siegel disks and basins of attraction for families of analytic functions. Izv. Sarat. Univ. (N.S.) Ser. Mat. Mekh. Inform. 5 (2005) No.1, 12-26 (in Russian) ISSN 1814-733X ISSN 1816-9791

2004:

•  A lower estimate for the distance of an attracting fixed point to the boundary of its basin via univalence radius. Comput. Methods Funct. Theory 3 (2004) No.2, 413-424. DOI 10.1007/BF03321046.

2002:

•  The Fatou and Julia sets of multivalued analytic functions. Sib. Mat. Zh. 43 (2002) No.6, 1293-1303; transl. in Sib. Math. J. 43 (2002) No.6, 1047-1054. DOI 10.1023/A:1021117301173. SibMatZh.pdf

1999:

• (with A. M. Zakharov and A. A. Kuznetsov) Extremal problems for a family of functionals and the Roth conjectures. Izv., Ross. Akad. Estestv. Nauk, Mat. Mat. Model. Inform. Upr. 3 (1999) No.2, 36-59 (in Russian; English summary) Zbl 0992.30011