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[506] Minimal surfaces with free boundaries

S. Hildebrandt University of Bonn, Bonn, F.R. Germany J. C. C. Nitsche University of Minnesota, Minneapolis, Minn., USA

TBD mathscidoc:1701.331559

Acta Mathematica, 143, (1), 251-272, 1979.4

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Michael Struwe. The existence of surfaces of constant mean curvature with free boundaries. 1988.

Grter M, Hildebrandt S, Nitsche J C, et al. On the boundary behavior of minimal surfaces with a free boundary which are not minima of the area[J]. Manuscripta Mathematica, 1981, 35(3): 387-410.

Struwe M. On a free boundary problem for minimal surfaces[J]. Inventiones Mathematicae, 1984, 75(3): 547-560.

Hildebrandt S, Nitsche J C. Optimal boundary regularity for minimal surfaces with a free boundary[J]. Manuscripta Mathematica, 1981: 357-364.

Hildebrandt S, Nitsche J C. A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles[J]. Archive for Rational Mechanics and Analysis, 1982, 79(3).

Hildebrandt S, Nitsche J C. Geometric properties of minimal surfaces with free boundaries[J]. Mathematische Zeitschrift, 1983, 184(4): 497-509.

Gruter M, Hildebrandt S, Nitsche J C, et al. Regularity for stationary surfaces of constant mean curvature with free boundaries[J]. Acta Mathematica, 2013, 156(1): 119-152.

Michael Struwe. The evolution of harmonic mappings with free boundaries. 1991.

Jost J. Continuity of minimal surfaces with piecewise smooth free boundaries[J]. Mathematische Annalen, 1987, 276(4): 599-614.

Li M. A General Existence Theorem for Embedded Minimal Surfaces with Free Boundary[J]. Communications on Pure and Applied Mathematics, 2012, 68(2): 286-331.

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[507] Nichtlineare Integralgleichungen nebst Anwendungen

A. Hammerstein Berlin

TBD mathscidoc:1701.33738

Acta Mathematica, 54, (1), 117-176, 1930.7

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Kot M, Schaffer W M. Discrete-time growth-dispersal models[J]. Bellman Prize in Mathematical Biosciences, 1986, 80(1): 109-136.

Hunt K J, Munih M, Donaldson N D, et al. Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle[J]. IEEE Transactions on Biomedical Engineering, 1998, 45(8): 998-1009.

Dolph C L. Nonlinear integral equations of the Hammerstein type[J]. Transactions of the American Mathematical Society, 1949, 66(2): 289-307.

Lazer A C, Mckenna P J. On a conjecture related to the number of solutions of a nonlinear Dirichlet problem[J]. Proceedings of The Royal Society of Edinburgh Section A-mathematics, 1983: 275-283.

Felix E Browder · Chaitan P Gupta. Monotone operators and nonlinear integral equations of Hammerstein type. 1969.

Mawhin J. Periodic oscillations of forced pendulum-like equations[J]. Lecture Notes in Mathematics, 1982: 458-476.

Schiffer M, Hawley N S. Connections and conformal mapping[J]. Acta Mathematica, 1961: 175-274.

Browder F E. Nonlinear Functional Analysis and Nonlinear Integral Equations of Hammerstein and Urysohn Type[C]., 1971: 425-500.

Yee K S. Numerical solution of initial boundary value problems involving maxwell\u0027s equations in isotropic media[J]. IEEE Transactions on Antennas and Propagation, 1966, 14(3): 302-307.

Faugeras O, Veltz R, Grimbert F, et al. Persistent neural states: Stationary localized activity patterns in nonlinear continuous n-population, q-dimensional neural networks[J]. Neural Computation, 2009, 21(1): 147-187.

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[508] A Beurling-type theorem

Boris Korenblum Tel-Aviv University, Tel-Aviv, Israel

TBD mathscidoc:1701.331512

Acta Mathematica, 138, (1), 265-293, 1975.11

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David Bekolle. Theory of Bergman Spaces. 2008.

Alexander Borichev · Ha Kan Hedenmalm. Harmonic functions of maximal growth: invertibility and cyclicity in Bergman spaces. 1997.

Bell S R, Boas H P. Regularity of the Bergman projection and duality of holomorphic function spaces[J]. Mathematische Annalen, 1984, 267(4): 473-478.

Korenblum B. Cyclic elements in some spaces of analytic functions[J]. Bulletin of the American Mathematical Society, 1981, 5(3): 317-318.

Shields A L. Cyclic Vectors in Banach Spaces of Analytic Functions[C]., 1985: 315-349.

Leon Brown · Boris Korenblum. Cyclic vectors in. 1988.

Korenblum B. A generalization of two classical convergence tests for Fourier series, and some new Banach spaces of functions[J]. Bulletin of the American Mathematical Society, 1983, 9(2): 215-218.

Korenblum B. On a class of Banach spaces of functions associated with the notion of entropy[J]. Transactions of the American Mathematical Society, 1985, 290(2): 527-553.

S N Melikhov. (DFS)-spaces of holomorphic functions invariant under differentiation. 2004.

Khoi L H, Thomas P. Weakly sufficient sets for A−∞(D)[J]. Publicacions Matematiques, 1998, 42(2): 435-448.

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[509] Zur Theorie der Meromorphen Funktionen

Rolf Nevanlinna Helsingfors

TBD mathscidoc:1701.33635

Acta Mathematica, 46, (1), 1-99, 1925.6

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Fay T H. Convex functions[J]. Mathematics and Computer Education, 1998.

Halburd R G, Korhonen R. Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations[J]. Journal of Mathematical Analysis and Applications, 2005, 314(2): 477-487.

Halburd R G, Korhonen R. Nevanlinna theory for the difference operator[C]., 2005, 31(2): 463-478.

Shimizu T. On the Theory of Meromorphic Functions[J]. Proceedings of The Imperial Academy, 1929, 5(3): 105-107.

Osgood C F. Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better[J]. Journal of Number Theory, 1985, 21(3): 347-389.

R G Halburd · Risto Korhonen. Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations. 2007.

Mathieu Meyer. Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie. 1986.

Halburd R G, Korhonen R, Tohge K, et al. Holomorphic curves with shift-invariant hyperplane preimages[J]. Transactions of the American Mathematical Society, 2009, 366(8): 4267-4298.

Gundersen G G, Hayman W K. The Strength of Cartan\u0027s Version of Nevanlinna Theory[J]. Bulletin of The London Mathematical Society, 2004, 36(4): 433-454.

Constales D, De Almeida R, Kraushar R S, et al. On Cauchy estimates and growth orders of entire solutions of iterated Dirac and generalized Cauchy–Riemann equations[J]. Mathematical Methods in The Applied Sciences, 2006, 29(14): 1663-1686.

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[510] Separatrices at singular points of planar vector fields

Stephen Schecter North Carolina State University, Raleigh, NC, USA Michael F. Singer North Carolina State University, Raleigh, NC, USA

TBD mathscidoc:1701.331571

Acta Mathematica, 145, (1), 47-78, 1979.2

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Jiang Q, Llibre J. Qualitative Classification of Singular Points[J]. Qualitative Theory of Dynamical Systems, 2005, 6(1): 87-168.

Enciso A, Peraltasalas D. Critical points of Green\u0027s functions on complete manifolds[J]. Journal of Differential Geometry, 2010, 92(1): 1-29.

Marek Izydorek · Slawomir Rybicki · Zbigniew Szafraniec. A note on the Poincaré-Bendixson index theorem. 1996.

Schecter S, Singer M F. Singular points of planar vector fields[C]., 1980: 393-409.

Sverdlove R. Critical points with asymmetric schemes[J]. Journal of Mathematical Analysis and Applications, 1982, 88(2): 452-463.

Stephen Schecter · Michael F Singer. Erratum to: Separatrices at singular points of planar vector fields. 2006.

Stephen Schecter · Michael F Singer. Correction to Separatrices at singular points of planar vector fields. 1983.

Antonio Algaba · Isabel Checa · Cristobal Garcia · Manuel L Reyes. Local Phase Portraits through the Newton Diagram of a Vector Field. 2015.

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TBD

[506] Minimal surfaces with free boundaries

S. Hildebrandt University of Bonn, Bonn, F.R. Germany J. C. C. Nitsche University of Minnesota, Minneapolis, Minn., USA

TBD mathscidoc:1701.331559

[507] Nichtlineare Integralgleichungen nebst Anwendungen

A. Hammerstein Berlin

TBD mathscidoc:1701.33738

[508] A Beurling-type theorem

Boris Korenblum Tel-Aviv University, Tel-Aviv, Israel

TBD mathscidoc:1701.331512

[509] Zur Theorie der Meromorphen Funktionen

Rolf Nevanlinna Helsingfors

TBD mathscidoc:1701.33635

[510] Separatrices at singular points of planar vector fields

Stephen Schecter North Carolina State University, Raleigh, NC, USA Michael F. Singer North Carolina State University, Raleigh, NC, USA

TBD mathscidoc:1701.331571

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