The Bernstein Conjecture, Minimal Cones, and Critical Dimensions

D. J. Korteweg, “Sur la forme que prennat les équations du mouvement des fluides si l’on tient compte des forces capilaires causées par des variations de density”, Archives Nèerlandaise des Science Exactes et Naturelles 6

1901

Earlier work this paper cites.

W. W. Mullins, “Theory of Thermal Grooving”, J. Appl. Phys. 28

1957

Earlier work this paper cites.

E. Bombieri, E. de Giorgi and E. Giusti, “Minimal Cones and the Bernstein Problem”, Inventiones math

1969

Earlier work this paper cites.

R. Schoen and S. T. Yau, “Positivity Of The Total Mass Of A General Space-Time,” Phys. Rev. Lett. 43

1979

Earlier work this paper cites.

S. Allen and J. W. Cahn, “A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening”, Acta Metall., 27

1979

Earlier work this paper cites.

E. de Giorgi, “Convergence problems for functionals and operators”, Proc. Int. Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), 131-188, Pitagora, Bologna (1979)

1979

Earlier work this paper cites.

P. Breitenlohner and D. Z. Freedman, “Positive Energy In Anti-De Sitter Backgrounds And Gauged Extended Supergravity,” Phys. Lett. B 115

1982

Earlier work this paper cites.

H. E. Rauch, “Geodesic and Curvature in Differential Geometry in the Large”, Graduate School of Mathematical Sciences, Yeshiva University, New York (1959); M. M. Postnikov, “The Variational Theory of Geodesics”, Dover Publications (1983)

1983

Earlier work this paper cites.

J. Serrin, “The form of interfacial surfaces in Korteweg’s theory of phase equilibria”, Quart. Appl. Math. 41

1983

Cited alongside, same era.

Pucci, “Patrizia An overdetermined system”, Quart. Appl. Math. 41

Original

1983

Cited alongside, same era.

A. T. Fomenko, “The Plateau Problem: Part II the present state of the theory”, Studies in the Development of Modern Mathematics Volume 1, Gordon and Breach Science Publishers (1990)

1990

Cited alongside, same era.

Dao Trong Thi and A. T. Fomenko, “Minimal surfaces, stratified multivarifolds, and the plateau problem”, Translations of mathematical monographs, AMS, 84

1991

Cited alongside, same era.

M. W. Choptuik, “Universality And Scaling In Gravitational Collapse Of A Massless Scalar Field,” Phys. Rev. Lett. 70

1993

G. W. Gibbons, S. A. Hartnoll and C. N. Pope, “Bohm and Einstein-Sasaki metrics, black holes and cosmological event horizons,” Phys. Rev. D 67

2003

Later among the works it cites.

B. Kol, “Topology change in general relativity and the black-hole black-string transition,” JHEP 0510

2005

Later among the works it cites.

E. Sorkin, “A critical dimension in the black-string phase transition,” Phys. Rev. Lett. 93

2005

Later among the works it cites.

V. P. Frolov, “Merger transitions in brane-black-hole systems: Criticality, scaling, and self-similarity,” Phys. Rev. D 74

2006

Later among the works it cites.

D. Mateos, R. C. Myers and R. M. Thomson, “Holographic phase transitions with fundamental matter,” Phys. Rev. Lett. 97

2007

Later among the works it cites.