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On the injectivity radius in Hofer's geometry
Globally subanalytic CMC surfaces in $\mathbb{R}^3$
1. | Rua Carolina Sucupira 723 ap 2002, 60140-120, Fortaleza-CE, Brazil |
2. | Departamento de Matemática, Universidade Federal do Ceará Av. Hum- berto Monte, s/n Campus do Pici - Bloco 914, 60455-760, Fortaleza-CE, Brazil |
3. | Instituto Nacional de Matemática Pura e Aplicada, IMPA Estrada Dona Castorina 110, 22460-320, Rio de Janeiro-RJ, Brazil |
4. | Departamento de Matemática, Universidade Federal do Ceará Av. Humberto Monte, s/n Campus do Pici - Bloco 914, 60455-760, Fortaleza-CE, Brazil |
References:
[1] |
A. Alexandrov, A characteristic property of spheres, Ann. Mat. Pura Appl., 58 (1962), 303-315.
doi: 10.1007/BF02413056. |
[2] |
J. Barbosa and M. do Carmo, On regular algebraic surfaces of $\mathbb{R}^3$ with constant mean curvature, arXiv:1403.7029, (2014). |
[3] |
E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math., 67 (1988), 5-42. |
[4] |
M. Coste, An Introduction to Semialgebraic Geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa, 2000. Available from: http://perso.univ-rennes1.fr/michel.coste/articles.html. |
[5] |
M. Coste, An Introduction to O-minimal Geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa, 2000. Available from: http://perso.univ-rennes1.fr/michel.coste/articles.html. |
[6] |
L. van den Dries, A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bulletin Amer. Math. Soc. (N.S.), 15 (1986), 189-193.
doi: 10.1090/S0273-0979-1986-15468-6. |
[7] |
L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J., 84 (1996), 467-540.
doi: 10.1215/S0012-7094-96-08416-1. |
[8] |
A. Gabrièlov, Projections of semianalytic sets, Funkcional. Anal. i Priložen., 2 (1968), 18-30. |
[9] |
H. Hopf, Über Flächen mit einer Relation zwischen Hauptkrümmungen, Math Nachr., 4 (1951), 232-249. |
[10] |
D. Hoffman and W. H. Meeks, III, The strong halfspace theorem for minimal surfaces, Invent. Math., 101 (1990), 373-377.
doi: 10.1007/BF01231506. |
[11] |
N. Korevaar, R. Kusner and B. Solomon, The struture of complete embedded surfaces with constant mean curvature, J. Differential Geom., 30 (1989), 465-503. |
[12] |
S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa (3), 18 (1964), 449-474. |
[13] |
R. Osserman, Global properties of minimal surfaces in $E^3$ and $E^n$, Ann. of Math. (2), 80 (1964), 340-364.
doi: 10.2307/1970396. |
[14] |
R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom., 18 (1983), 791-809. |
[15] |
A. Tarski, A Decision Method for an Elementary Algebra and Geometry, 2nd edition, University of California Press, Berkeley and Los Angeles, Calif., 1951. |
show all references
References:
[1] |
A. Alexandrov, A characteristic property of spheres, Ann. Mat. Pura Appl., 58 (1962), 303-315.
doi: 10.1007/BF02413056. |
[2] |
J. Barbosa and M. do Carmo, On regular algebraic surfaces of $\mathbb{R}^3$ with constant mean curvature, arXiv:1403.7029, (2014). |
[3] |
E. Bierstone and P. D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math., 67 (1988), 5-42. |
[4] |
M. Coste, An Introduction to Semialgebraic Geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa, 2000. Available from: http://perso.univ-rennes1.fr/michel.coste/articles.html. |
[5] |
M. Coste, An Introduction to O-minimal Geometry, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica, Istituti Editoriali e Poligrafici Internazionali, Pisa, 2000. Available from: http://perso.univ-rennes1.fr/michel.coste/articles.html. |
[6] |
L. van den Dries, A generalization of the Tarski-Seidenberg theorem, and some nondefinability results, Bulletin Amer. Math. Soc. (N.S.), 15 (1986), 189-193.
doi: 10.1090/S0273-0979-1986-15468-6. |
[7] |
L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J., 84 (1996), 467-540.
doi: 10.1215/S0012-7094-96-08416-1. |
[8] |
A. Gabrièlov, Projections of semianalytic sets, Funkcional. Anal. i Priložen., 2 (1968), 18-30. |
[9] |
H. Hopf, Über Flächen mit einer Relation zwischen Hauptkrümmungen, Math Nachr., 4 (1951), 232-249. |
[10] |
D. Hoffman and W. H. Meeks, III, The strong halfspace theorem for minimal surfaces, Invent. Math., 101 (1990), 373-377.
doi: 10.1007/BF01231506. |
[11] |
N. Korevaar, R. Kusner and B. Solomon, The struture of complete embedded surfaces with constant mean curvature, J. Differential Geom., 30 (1989), 465-503. |
[12] |
S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa (3), 18 (1964), 449-474. |
[13] |
R. Osserman, Global properties of minimal surfaces in $E^3$ and $E^n$, Ann. of Math. (2), 80 (1964), 340-364.
doi: 10.2307/1970396. |
[14] |
R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom., 18 (1983), 791-809. |
[15] |
A. Tarski, A Decision Method for an Elementary Algebra and Geometry, 2nd edition, University of California Press, Berkeley and Los Angeles, Calif., 1951. |
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