Hereditary circularity for energy minimal diffeomorphisms
HTML articles powered by AMS MathViewer
- by Ngin-Tee Koh PDF
- Conform. Geom. Dyn. 21 (2017), 369-377 Request permission
Abstract:
We reveal some geometric properties of energy minimal diffeomorphisms defined on an annulus, whose existence was established in works by Iwaniec et al. (2011) and Kalaj (2014).References
- Martin Chuaqui, Peter Duren, and Brad Osgood, Ellipses, near ellipses, and harmonic Möbius transformations, Proc. Amer. Math. Soc. 133 (2005), no. 9, 2705–2710. MR 2146217, DOI 10.1090/S0002-9939-05-07817-2
- J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3–25. MR 752388, DOI 10.5186/aasfm.1984.0905
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Peter L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
- Peter Duren, Harmonic mappings in the plane, Cambridge Tracts in Mathematics, vol. 156, Cambridge University Press, Cambridge, 2004. MR 2048384, DOI 10.1017/CBO9780511546600
- A. W. Goodman and E. B. Saff, On univalent functions convex in one direction, Proc. Amer. Math. Soc. 73 (1979), no. 2, 183–187. MR 516461, DOI 10.1090/S0002-9939-1979-0516461-2
- Erhard Heinz, On one-to-one harmonic mappings, Pacific J. Math. 9 (1959), 101–105. MR 104933, DOI 10.2140/pjm.1959.9.101
- W. Hengartner and G. Schober, A remark on level curves for domains convex in one direction, Applicable Anal. 3 (1973), 101–106. MR 393450, DOI 10.1080/00036817308839059
- W. Hengartner and G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. (2) 33 (1986), no. 3, 473–483. MR 850963, DOI 10.1112/jlms/s2-33.3.473
- Walter Hengartner and Glenn Schober, Univalent harmonic exterior and ring mappings, J. Math. Anal. Appl. 156 (1991), no. 1, 154–171. MR 1102603, DOI 10.1016/0022-247X(91)90388-G
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- Tadeusz Iwaniec, Ngin-Tee Koh, Leonid V. Kovalev, and Jani Onninen, Existence of energy-minimal diffeomorphisms between doubly connected domains, Invent. Math. 186 (2011), no. 3, 667–707. MR 2854087, DOI 10.1007/s00222-011-0327-6
- Tadeusz Iwaniec, Leonid V. Kovalev, and Jani Onninen, The Nitsche conjecture, J. Amer. Math. Soc. 24 (2011), no. 2, 345–373. MR 2748396, DOI 10.1090/S0894-0347-2010-00685-6
- David Kalaj, Energy-minimal diffeomorphisms between doubly connected Riemann surfaces, Calc. Var. Partial Differential Equations 51 (2014), no. 1-2, 465–494. MR 3247397, DOI 10.1007/s00526-013-0683-8
- Ngin-Tee Koh, Hereditary convexity for harmonic homeomorphisms, Indiana Univ. Math. J. 64 (2015), no. 1, 231–243. MR 3320525, DOI 10.1512/iumj.2015.64.5282
- Ngin-Tee Koh, Harmonic mappings with hereditary starlikeness, J. Math. Anal. Appl. 457 (2018), no. 1, 273–286. MR 3702706, DOI 10.1016/j.jmaa.2017.08.032
- N.-T. Koh and L. V. Kovalev, Area contraction for harmonic automorphisms of the disk, Bull. Lond. Math. Soc. 43 (2011), no. 1, 91–96. MR 2765553, DOI 10.1112/blms/bdq083
- O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 126, Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by K. W. Lucas. MR 0344463, DOI 10.1007/978-3-642-65513-5
- Zeev Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1952. MR 0045823
- E. Study, Vorlesungen über ausgewählte Gegenstände der Geometrie, Heft II, Teubner, Leipzig, 1913.
Additional Information
- Ngin-Tee Koh
- Affiliation: School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
- MR Author ID: 871815
- Email: ngin-tee.koh@canterbury.ac.nz
- Received by editor(s): November 1, 2016
- Received by editor(s) in revised form: August 20, 2017
- Published electronically: December 13, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Conform. Geom. Dyn. 21 (2017), 369-377
- MSC (2010): Primary 30C45, 31A05, 34B24
- DOI: https://doi.org/10.1090/ecgd/315
- MathSciNet review: 3735455