On nonparametric surfaces of constant mean curvature

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1. [1] S. Bernstein, Sur les surfaces definies au moyen de leur courbure moyenne et totale, Ann. Sci. Ecole Norm. Sup., 27 (1910), pp. 233-256. Zbl41.0692.05MR1509123JFM41.0692.05
2. [2] E. Heinz, Über Flächen mit eineindeutiger Projektion auf eine Ebene, deren Krümmung durch Ungleichungen eingeschränkt sind, Math. Ann., 129 (1955), pp. 451-454. Zbl0065.37201MR71822
3. [3] S.S. Chern, On the curvature of a piece of hypersurface in Euclidian space, Abh. Math. Sem. Univ. Hamburg, 29 (1965), pp. 77-91. Zbl0147.20901MR188949
4. [4] R. Finn, Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature, J. D'Anal. Math., 14 (1965), pp. 139-160. Zbl0163.34604MR188909
5. [5] J. Spruck, Infinite boundary value problems for surfaces of constant mean curvature, Arch. Rat. Mech. Anal., 49 (1972), pp. 1-31. Zbl0263.53008MR334010
6. [6] R. Finn, New estimates for equations of minimal surface type, Arch. Rat. Mech. Anal., 14 (1963), pp. 337-375. Zbl0133.04601MR157096
7. [7] S. Bernstein, Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Zeit., 26 (1927), pp. 551-558. Zbl53.0670.01MR1544873JFM53.0670.01
8. [8] E. Heinz, Über die Lösungen der Minimalflächengleichung, Gott. Nach. (1952), pp. 51-56. Zbl0048.15401MR54182
9. [9] E. Hopf, On an inequality for minimal surfaces z = z(x, y), J. Rat. Mech. Anal., 2 (1953), pp. 519-522. Zbl0051.12601MR55735
10. [10] R. Finn - R. Ossfrman, On the Gauss curvature of nonparametric minimal surfaces, J. d'Anal. Math., 12 (1964), pp. 351-364. Zbl0122.16404MR166694
11. [11] J. Spruck, An a priori estimate for the Gauss curvature of nonparametric surfaces of constant mean curvature, Proc. Amer. Math. Soc., 36 (1972), pp. 217-223. Zbl0256.53007MR307056
12. [12] J. Spruck, Gauss curvature estimates for surfaces of constant mean curvature, to appear. Zbl0276.53002MR367881
13. [13] R. Finn, On equations of minimal surface type, Annals of Math., 60 (1954), pp. 397-416. Zbl0058.32501MR66533
14. [14] R. Finn, A note on the capillary problem, Acta Math., 132 (1974), pp. 199-205. Zbl0382.76004MR670442
15. [15] J. Sfrrin, The Dirichlet problem for surfaces of constant mean curvature, Proc. London Math. Soc. III Ser., 21 (1970), pp. 361-384. Zbl0199.16604MR275336
16. [16] O.A. Ladyzhenskaia - N.N. Ural'tseva, Local estimates for the gradients of nonuniformly elliptic and parabolic equations, Comm. Pure Appl. Math., 23 (1970), pp. 677-703. Zbl0193.07202MR265745
17. [17] E. Heinz, Interior gradient estimates for surfaces z = f(x, y) with prescribed mean curvature, J. Diff. Geom., 5 (1971), pp. 149-157. Zbl0212.44001MR289940
18. [18] E. Bombieri - E. Giusti, Local estimates for the gradient of non-parametric surfaces of prescribed mean curvature, Comm. Pure Appl. Math., 26 (1973), pp. 381-394. Zbl0266.53042MR344977
19. [19] N.S. Trudinger, Gradient estimates and mean curvature, Math. Zeit., 131 (1973), pp. 165-175. Zbl0253.53003MR324187
20. [20] E. Giusti, Boundary value problems for non-parametric surfaces of prescribed mean curvature, Ann. Scuola Norm. Sup. Pisa, 3 (1976) pp. 501-548. Zbl0344.35036MR482506
21. [21] M. Miranda, Distribuzioni aventi derivate misure e insiemi di perimetro localmente finito, Ann. Scuola Norm. Sup., Pisa, 18 (1964), pp. 27-56. Zbl0131.11802MR165073
22. [22] E. De Giorgi, Su una teoria generale della misura (r — 1) dimensionale in uno spazio ad r dimensioni, Annali di mat. pura ed appl., Ser. 4, 36 (1964), pp. 191-213. Zbl0055.28504MR62214
23. [23] M. Miranda, Analiticità delle superfici di area minima in R4, Rend. Acc. Naz. Lincei, 38 (1965), pp. 632-638. Zbl0135.32601MR193579
24. [24] M. Miranda, Superfici minime con ostacoli, Ann. Univ. Ferrara VII(N.S.), 16 (1971), pp. 29-37. Zbl0266.49036MR301617
25. [25] M. Miranda, Superfici minime illimitate, to appear in Ann. Scuola Norm. Sup. Pisa. Zbl0352.49020MR500423

1. Kok Seng Chua, Absolute gradient bound for surfaces of constant mean curvature
2. Enrico Giusti, Boundary value problems for non-parametric surfaces of prescribed mean curvature
3. Fei-Tsen Liang, Harnack’s inequalities for solutions to the mean curvature equation and to the capillarity problem