×

zbMATH — the first resource for mathematics

An a priori estimate for the Gauss curvature of nonparametric surfaces of constant mean curvature. (English) Zbl 0256.53007

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
35B45 A priori estimates in context of PDEs
35G30 Boundary value problems for nonlinear higher-order PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ch. Delaunay, Sur la surface de revolution dont la courbure moyenne est constante J. Math. Pures Appl. 6 (1841), 309-315.
[2] Robert Finn, Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature, J. Analyse Math. 14 (1965), 139 – 160. · Zbl 0163.34604 · doi:10.1007/BF02806384 · doi.org
[3] R. Finn and R. Osserman, On the Gauss curvature of non-parametric minimal surfaces, J. Analyse Math. 12 (1964), 351 – 364. · Zbl 0122.16404 · doi:10.1007/BF02807440 · doi.org
[4] Erhard Heinz, Über die Lösungen der Minimalflächengleichung, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt. 1952 (1952), 51 – 56 (German). · Zbl 0048.15401
[5] Louis Nirenberg, On nonlinear elliptic partial differential equations and Hölder continuity, Comm. Pure Appl. Math. 6 (1953), 103 – 156; addendum, 395. · Zbl 0050.09801 · doi:10.1002/cpa.3160060105 · doi.org
[6] Johannes C. C. Nitsche, On new results in the theory of minimal surfaces, Bull. Amer. Math. Soc. 71 (1965), 195 – 270. · Zbl 0135.21701
[7] Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. · Zbl 0209.52901
[8] James Serrin, The Dirichlet problem for surfaces of constant mean curvature, Proc. London Math. Soc. (3) 21 (1970), 361 – 384. · Zbl 0199.16604 · doi:10.1112/plms/s3-21.2.361 · doi.org
[9] Joel Spruck, Infinite boundary value problems for surfaces of constant mean curvature, Arch. Rational Mech. Anal. 49 (1972/73), 1 – 31. · Zbl 0263.53008 · doi:10.1007/BF00281471 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.