Minimal-area metrics on the Swiss cross and punctured torus

M. G. Katz and S. Sabourau, “Systolically extremal nonpositively curved surfaces are flat with finitely many singularities,” to appear in Journal of Topology and Analysis. DOI: 10.1142/S1793525320500144 [arXiv:1904.00730]

Original

1904

Earlier work this paper cites.

P. M. Pu, “Some inequalities in certain nonorientable Riemannian manifolds”, Pacific. J. Math. 2

1952

Earlier work this paper cites.

L. V. Ahlfors, Conformal Invariants: Topics in Geometric Function Theory

1973

Earlier work this paper cites.

M. Gromov, “Filling Riemannian Manifolds,” J. Differential Geom. 18

1983

Earlier work this paper cites.

K. Strebel, Quadratic differentials,

1984

Earlier work this paper cites.

M. Saadi and B. Zwiebach, “Closed String Field Theory from Polyhedra,” Annals Phys. 192

1989

Earlier work this paper cites.

T. Kugo, H. Kunitomo and K. Suehiro, “Nonpolynomial Closed String Field Theory,” Phys. Lett. B 226

1989

Earlier work this paper cites.

B. Zwiebach, “Consistency of Closed String Polyhedra From Minimal Area,” Phys. Lett. B 241

1990

Earlier work this paper cites.

B. Zwiebach, “How Covariant Closed String Theory Solves A Minimal Area Problem,” Commun. Math. Phys. 136

1991

Cited alongside, same era.

K. Strebel, private communication to B. Zwiebach (1991)

1991

Cited alongside, same era.

K. Ranganathan, “A Criterion for flatness in minimal area metrics that define string diagrams,” Commun. Math. Phys. 146

1992

Cited alongside, same era.

B. Zwiebach, “Quantum open string theory with manifest closed string factorization,” Phys. Lett. B 256

1992

Cited alongside, same era.

B. Zwiebach, “Closed string field theory: Quantum action and the B-V master equation,” Nucl. Phys. B 390

1993

Cited alongside, same era.

M. Wolf and B. Zwiebach, “The Plumbing of minimal area surfaces,” Journal of Geometry and Physics 15

R. L. Bryant, “On extremal with prescribed Lagrangian densities,” in “Manifolds and Geometry” (Pisa, 1993), Cambridge University Press, 1996. arXiv:dg-ga/9406001

1996

Later among the works it cites.

S. Marnerides, “The minimal-area problem of closed string field theory”, Bachelor of science thesis, MIT (2003)

2003

Later among the works it cites.

S. Boyd and L. Vandenberghe, Convex Optimization

2004

Later among the works it cites.

M. G. Katz, Systolic Geometry and Topology,

2007

Later among the works it cites.

B. Shapiro, S. Agarwal, L. Robison, K. Zhu, C. Spires, “Geometric calculus of variation: Vigre Summer 2011” Rice University (2011). https://cnx.org/contents/PVRJksOK@1/Geometric-Calculus-of-Variatio

2011

Later among the works it cites.