References
V. Benci & J. M. Coron, The Dirichlet problem for harmonic maps from the disk into the Euclidean n-sphere. Ann. I.H.P. Analyse Nonlinéaire (to appear).
H. Brezis & J. M. Coron, Multiple solutions of H-systems and Rellich's conjecture. Comm. Pure Appl. Math. 37 (1984), 149–187. See also Sur la conjecture de Rellich pour les surfaces à courbure moyenne prescrite. C. R. Acad. Sc. Paris 295 (1982), 615–618.
H. Brezis & J. M. Coron, Convergence de solutions de H-systèmes et application aux surfaces a courbure moyenne constante. C. R. Acad. Sc. Paris 298 (1984), 389–392.
H. Brezis & E. H. Lieb, Minimum action solutions of some vector field equations. Comm. Math. Phys. (to appear).
B. Gidas, W. M. Ni & L. Nirenberg, Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979), 200–243.
R. D. Gulliver, R. Osserman & H. L. Royden, A theory of branched immersions of surfaces. Amer. J. Math. 95 (1973), 750–812.
E. Heinz, Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung. Math. Ann. 127 (1954), 258–287.
S. Hildebrandt, On the Plateau problem for surfaces of constant mean curvature. Comm. Pure Appl. Math. 23 (1970), 97–114.
S. Hildebrandt, Nonlinear elliptic systems and harmonic mappings. Proc. 1980 Beijing Symp. Diff. Geom. and Diff. Eq., S. S. Chern and Wu Wen-tsün ed. Science Press Beijing (1982) and Gordon-Breach.
J. Jost, Harmonic mappings between surfaces. Lectures notes in Math. Volume 1062, Springer (1984).
L. Lemaire, Applications harmoniques de surfaces Riemanniennes. J. Diff. Geometry 13 (1978), 51–78.
E. H. Lieb, On the lowest eigenvalue of the laplacian for the intersection of two domains. Invent. Math. 74 (1983), 441–448.
P. L. Lions, Principe de concentration-compacité en calcul des variations. C. R. Acad. Sci. Paris 294 (1982), 261–264. The concentration-compactness principle in the calculus of variations: the locally compact case. Part I, Ann. I.H.P. Analyse Non-linéaire 1 (1984), 109–145 and Part II 1 (1984), 223–283.
P. L. Lions, Applications de la méthode de concentration compacité à l'existence de fonctions extrémales. C. R. Acad. Sci. Paris 296 (1983) p. 645–648. The concentration-compactness principle in the calculus of variations: the limit case. Parts I and II, Riv. Iberoamericana (to appear).
W. Meeks & S. T. Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Annals of Math. 112 (1980), 441–484.
E. A. Ruh, Asymptotic behaviour of non-parametric minimal hypersurfaces. J. Diff. Geometry, 4 (1970), 509–513.
J. Sacks & K. Uhlenbeck, The existence of minimal immersions of 2-spheres. Ann. Math. 113 (1981), 1–24.
J. Serrin, On surfaces of constant mean curvature which span a given space curve. Math. Z. 112 (1969), 77–88.
Y.-T. Siu & S. T. Yau. Compact Kähler manifolds of positive bisectional curvature. Invent. Math. 59 (1980), 189–204.
G. Springer, Introduction to Riemann surfaces. Addison-Wesley, Reading MA-London (1957).
K. Steffen, Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Archive Rational Mech. Anal. 49 (1972), 99–128.
K. Steffen, On the nonuniqueness of surfaces with prescribed mean curvature spanning a given contour, (to appear).
M. Struwe, Non uniqueness in the Plateau problem for surfaces of constant mean curvature, (to appear).
M. Struwe, A global existence result for elliptic boundary value problems involving limiting nonlinearities, (to appear).
C. H. Taubes, Path connected Yang-Mills moduli spaces. J. Diff. Geom. (to appear).
H. Wente, An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl. 26 (1969), 318–344.
H. Wente, The differential equation 56–01 with vanishing boundary values. Proc. A.M.S. 50 (1975), 131–137.
H. Wente, Large solutions to the volume constrainted Plateau proplem. Arch. Rational Mech. Anal. 75 (1980), 59–77.
H. Werner, Das Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann. 133 (1957), 303–319.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brezis, H., Coron, J.M. Convergence of solutions of H-systems or how to blow bubbles. Arch. Rational Mech. Anal. 89, 21–56 (1985). https://doi.org/10.1007/BF00281744
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281744