Embedding Riemann surfaces with isolated punctures into the complex plane
HTML articles powered by AMS MathViewer
- by Frank Kutzschebauch and Pierre-Marie Poloni PDF
- Proc. Amer. Math. Soc. 148 (2020), 4831-4835 Request permission
Abstract:
We enlarge the class of open Riemann surfaces known to be holomorphically embeddable into the plane by allowing them to have additional isolated punctures compared to the known embedding results.References
- Steven R. Bell and Raghavan Narasimhan, Proper holomorphic mappings of complex spaces, Several complex variables, VI, Encyclopaedia Math. Sci., vol. 69, Springer, Berlin, 1990, pp. 1–38. MR 1095089
- Franc Forstnerič, Stein manifolds and holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 56, Springer, Heidelberg, 2011. The homotopy principle in complex analysis. MR 2975791, DOI 10.1007/978-3-642-22250-4
- Franc Forstnerič and Erlend Fornæss Wold, Bordered Riemann surfaces in $\Bbb C^2$, J. Math. Pures Appl. (9) 91 (2009), no. 1, 100–114 (English, with English and French summaries). MR 2487902, DOI 10.1016/j.matpur.2008.09.010
- Franc Forstnerič and Erlend Fornæss Wold, Embeddings of infinitely connected planar domains into ${\Bbb C}^2$, Anal. PDE 6 (2013), no. 2, 499–514. MR 3071396, DOI 10.2140/apde.2013.6.499
- Frank Kutzschebauch, Erik Løw, and Erlend Fornæss Wold, Embedding some Riemann surfaces into $\Bbb C^2$ with interpolation, Math. Z. 262 (2009), no. 3, 603–611. MR 2506310, DOI 10.1007/s00209-008-0392-8
- Avinash Sathaye, On planar curves, Amer. J. Math. 99 (1977), no. 5, 1105–1135. MR 466148, DOI 10.2307/2374003
- Erlend Fornæss Wold, Proper holomorphic embeddings of finitely and some infinitely connected subsets of $\Bbb C$ into $\Bbb C^2$, Math. Z. 252 (2006), no. 1, 1–9. MR 2209147, DOI 10.1007/s00209-005-0836-3
- Erlend Fornæss Wold, Embedding Riemann surfaces properly into $\Bbb C^2$, Internat. J. Math. 17 (2006), no. 8, 963–974. MR 2261643, DOI 10.1142/S0129167X06003746
- Erlend Fornæss Wold, Embedding subsets of tori properly into $\Bbb C^2$, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 5, 1537–1555 (English, with English and French summaries). MR 2364141
Additional Information
- Frank Kutzschebauch
- Affiliation: Departement Mathematik, Universität Bern, Sidlerstrasse 5, CH–3012 Bern, Switzerland
- MR Author ID: 330461
- Email: frank.kutzschebauch@math.unibe.ch
- Pierre-Marie Poloni
- Affiliation: Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH–4051 Basel, Switzerland
- MR Author ID: 800101
- Email: poloni.pierremarie@gmail.com
- Received by editor(s): February 21, 2020
- Received by editor(s) in revised form: March 22, 2020
- Published electronically: August 4, 2020
- Additional Notes: The first author was partially supported by Schweizerischer Nationalfonds Grant 200021-116165.
- Communicated by: Filippo Bracci
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4831-4835
- MSC (2010): Primary 32C22; Secondary 14H55, 32E10, 32Q40
- DOI: https://doi.org/10.1090/proc/15111
- MathSciNet review: 4143397