The boundary behavior of minimal surfaces. Kellogg's theorem and branch points on the boundary
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Minimal Surface Branch Point Boundary Behavior
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Bibliography
- 1.Courant, R.: Dirichlet's principle, conformal mapping, and minimal surfaces. New York: Interscience 1950.Google Scholar
- 2.Golusin, G. M.: Geometrische Funktionentheorie. Berlin: VEB Verlag 1957.Google Scholar
- 3.Hartman, P., Wintner, A.: On the local behavior of solutions of non-parabolic partial differential equations. Amer. J. Math.75, 449–476 (1953).Google Scholar
- 4.Heinz, E.: On certain nonlinear elliptic differential equations and univalent mappings. J. d'Anal. Math.5, 197–262 (1956/1957).Google Scholar
- 5.Heinz, E. Tomi, F.: Zu einem Satze von S. Hildebrandt über das Randverhalten von Minimalflächen. Math. Z. (to appear).Google Scholar
- 6.Hildebrandt, S.: Über das Randverhalten von Minimalflächen. Math. Ann.165, 1–18 (1966).Google Scholar
- 7.Hildebrandt, S.: Boundary behavior of minimal surfaces. Arch. Rat. Mech. Anal. (to appear).Google Scholar
- 8.Kellogg, O. D.: Harmonic functions and Green's integral. Transact. Amer. Math. Soc.13, 109–132 (1912).Google Scholar
- 9.Kinderlehrer, D. S.: Minimal surfaces whose boundaries contain spikes. J. Math. Mech. (to appear).Google Scholar
- 10.Ladyzhenskaya, O. A., Ural'tseva, N. N.: On the smoothness of weak solutions of quasilinear equations in several variables and of variational problems. Comm. P. Appl. Math.14, 481–495 (1961).Google Scholar
- 11.——: Linear and quasilinear elliptic equations. New York and London: Academic Press 1968.Google Scholar
- 12.Lebesgue, H.: Sur le problème de Dirichlet. Rend. Circ. Mat. Palermo24, 371–402 (1907).Google Scholar
- 13.Lewy, H.: On the boundary behavior of minimal surfaces. Proc. Nat. Acad. Sci. U.S.A.37, 103–110 (1951).Google Scholar
- 14.Morrey, C. B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966.Google Scholar
- 15.Nitsche, J. C. C.: On new resultat in the theory of minimal surfaces. Bull. Amer. Math. Soc.71, 195–270 (1965).Google Scholar
- 16.Riesz, F.: Über die Randwerte einer analytischen Funktion. Math. Z.18, 87–95 (1923).Google Scholar
- 17.Sasaki, S.: On the total curvature of a closed curve. Japan. J. Math.29, 118–125 (1959).Google Scholar
- 18.Tonelli, L.: Opere Scelte, vol. III. Roma: Ediz. Cremonese 1962.Google Scholar
- 19.Tsuji, M.: On a theorem of F. and M. Riesz. Proc. Imp. Acad. Tokyo18, 172–175 (1942).Google Scholar
- 20.—: Potential theory in modern function theory. Tokyo: Maruzen 1959.Google Scholar
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