Volume 22, issue 1 (2018)

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Complete minimal surfaces densely lying in arbitrary domains of $\mathbb{R}^n$

Antonio Alarcón and Ildefonso Castro-Infantes

Geometry & Topology 22 (2018) 571–590
Bibliography
1 A Alarcón, B Drinovec Drnovšek, F Forstnerič, F J López, Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves, Proc. Lond. Math. Soc. 111 (2015) 851 MR3407187
2 A Alarcón, I Fernández, F J López, Complete minimal surfaces and harmonic functions, Comment. Math. Helv. 87 (2012) 891 MR2984575
3 A Alarcón, F Forstnerič, Every bordered Riemann surface is a complete proper curve in a ball, Math. Ann. 357 (2013) 1049 MR3118624
4 A Alarcón, F Forstnerič, Null curves and directed immersions of open Riemann surfaces, Invent. Math. 196 (2014) 733 MR3211044
5 A Alarcón, F Forstnerič, The Calabi–Yau problem, null curves, and Bryant surfaces, Math. Ann. 363 (2015) 913 MR3412347
6 A Alarcón, F Forstnerič, Null holomorphic curves in 3 and applications to the conformal Calabi–Yau problem, from: "Complex geometry and dynamics" (editors J E Fornæss, M Irgens, E F Wold), Abel Symp. 10, Springer (2015) 101 MR3587463
7 A Alarcón, F Forstnerič, F J López, Embedded minimal surfaces in n, Math. Z. 283 (2016) 1 MR3489056
8 A Alarcón, F Forstnerič, F J López, New complex analytic methods in the study of non-orientable minimal surfaces in n, preprint (2016) arXiv:1603.01691
9 A Alarcón, F Forstnerič, F J López, Holomorphic Legendrian curves, Compos. Math. 153 (2017) 1945 MR3705282
10 A Alarcón, F J López, Minimal surfaces in 3 properly projecting into 2, J. Differential Geom. 90 (2012) 351 MR2916039
11 A Alarcón, F J López, Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into 2, J. Geom. Anal. 23 (2013) 1794 MR3107678
12 A Alarcón, F J López, Approximation theory for nonorientable minimal surfaces and applications, Geom. Topol. 19 (2015) 1015 MR3336277
13 P Andrade, A wild minimal plane in 3, Proc. Amer. Math. Soc. 128 (2000) 1451 MR1664289
14 E Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958) 29 MR0096818
15 B Drinovec Drnovšek, F Forstnerič, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007) 203 MR2352132
16 B Drinovec Drnovšek, F Forstnerič, The Poletsky–Rosay theorem on singular complex spaces, Indiana Univ. Math. J. 61 (2012) 1407 MR3085613
17 H M Farkas, I Kra, Riemann surfaces, 71, Springer (1992) MR1139765
18 F Forstnerič, Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis, 56, Springer (2011) MR2975791
19 F Forstnerič, Oka manifolds : from Oka to Stein and back, Ann. Fac. Sci. Toulouse Math. 22 (2013) 747 MR3137250
20 F Forstnerič, Surjective holomorphic maps onto Oka manifolds, from: "Complex and symplectic geometry" (editors D Angella, C Medori, A Tomassini), Springer INdAM Ser., Springer (2017)
21 F Forstnerič, F Lárusson, Survey of Oka theory, New York J. Math. 17A (2011) 11 MR2782726
22 F Forstnerič, J Winkelmann, Holomorphic discs with dense images, Math. Res. Lett. 12 (2005) 265 MR2150882
23 F Forstnerič, E F Wold, Bordered Riemann surfaces in 2, J. Math. Pures Appl. 91 (2009) 100 MR2487902
24 J A Gálvez, P Mira, Dense solutions to the Cauchy problem for minimal surfaces, Bull. Braz. Math. Soc. 35 (2004) 387 MR2106312
25 R C Gunning, H Rossi, Analytic functions of several complex variables, Prentice-Hall (1965) MR0180696
26 L Hörmander, An introduction to complex analysis in several variables, 7, North-Holland (1990) MR1045639
27 F Kutzschebauch, Flexibility properties in complex analysis and affine algebraic geometry, from: "Automorphisms in birational and affine geometry" (editors I Cheltsov, C Ciliberto, H Flenner, J McKernan, Y G Prokhorov, M Zaidenberg), Springer Proc. Math. Stat. 79, Springer (2014) 387 MR3229363
28 F Lárusson, What is an Oka manifold ?, Notices Amer. Math. Soc. 57 (2010) 50 MR2590114
29 S Lie, Beiträge zur Theorie der Minimalflächen, Math. Ann. 14 (1878) 331 MR1509986
30 F J López, Exotic minimal surfaces, J. Geom. Anal. 24 (2014) 988 MR3192303
31 S N Mergelyan, On the representation of functions by series of polynomials on closed sets, Doklady Akad. Nauk SSSR 78 (1951) 405 MR0041929
32 R Osserman, A survey of minimal surfaces, Dover Publications (1986) MR852409
33 C Runge, Zur Theorie der Analytischen Functionen, Acta Math. 6 (1885) 245 MR1554665
34 J Winkelmann, Non-degenerate maps and sets, Math. Z. 249 (2005) 783 MR2126216