Fetching the paper…
Reading the bibliography…
As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori.
Jean Leray and Jules Schauder, Topologie et équations fonctionnelles , Ann. Sci. École Norm. Sup. (3) 51
1934
Earlier work this paper cites.
D. A. Raikov, To [sic]
1946
Earlier work this paper cites.
J. D. Newburgh, The variation of spectra , Duke Math. J. 18
1951
Earlier work this paper cites.
James Eells, Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds , Amer. J. Math. 86
1964
Earlier work this paper cites.
A. Hulanicki, On symmetry of group algebras of discrete nilpotent groups , Studia Math. 35
1970
Earlier work this paper cites.
by same author, On the spectrum of convolution operators on groups with polynomial growth , Invent. Math. 17
1972
Earlier work this paper cites.
Jerry L. Kazdan and F. W. Warner, Curvature functions for compact 2 2 -manifolds , Ann. of Math. (2) 99
1974
Earlier work this paper cites.
D. J. Newman, A simple proof of Wiener’s 1 / f 1/f theorem , Proc. Amer. Math. Soc. 48
1975
Earlier work this paper cites.
Lars V. Ahlfors, Complex analysis , third ed., McGraw-Hill Book Co., New York, 1978, An introduction to the theory of analytic functions of one complex variable, International Series in Pure and Applied Mathematics. MR510197 (80c:30001)
1978
Earlier work this paper cites.
Alain Connes, C ∗ C^{\ast} algèbres et géométrie différentielle , C. R. Acad. Sci. Paris Sér. A-B 290
1980
Earlier work this paper cites.
M. Pimsner and D. Voiculescu, Exact sequences for K K -groups and Ext-groups of certain cross-product C ∗ C^{\ast} -algebras , J. Operator Theory 4
1980
Earlier work this paper cites.
Marc A. Rieffel, C ∗ C^{\ast} -algebras associated with irrational rotations , Pacific J. Math. 93
1981
Cited alongside, same era.
S. K. Berberian, The maximal ring of quotients of a finite von Neumann algebra , Rocky Mountain J. Math. 12
1982
Cited alongside, same era.
Richard Schoen and Karen Uhlenbeck, Regularity of minimizing harmonic maps into the sphere , Invent. Math. 78
1984
Cited alongside, same era.
Alain Connes and Marc A. Rieffel, Yang-Mills for noncommutative two-tori , Operator algebras and mathematical physics (Iowa City, Iowa, 1985), Contemp. Math., vol. 62, Amer. Math. Soc., Providence, RI, 1987, pp. 237–266. MR878383 (88b:58033)
1987
Cited alongside, same era.
by same author, The homotopy groups of the unitary groups of noncommutative tori , J. Operator Theory 17
1987
Cited alongside, same era.
Alain Connes, Michael R. Douglas, and Albert Schwarz, Noncommutative geometry and matrix theory: compactification on tori , J. High Energy Phys. (1998), no. 2, Paper 3, 35 pp. (electronic). MR1613978 (99b:58023)
1998
Later among the works it cites.
Ludwik Da̧browski, Thomas Krajewski, and Giovanni Landi, Some properties of nonlinear σ \sigma -models in noncommutative geometry , Internat. J. Modern Phys. B 14
1999
Later among the works it cites.
1999
Later among the works it cites.
by same author, Non-linear σ \sigma -models in noncommutative geometry: fields with values in finite spaces , Modern Phys. Lett. A 18
2003
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
J.-B. Bost, Principe d’Oka, K K -théorie et systèmes dynamiques non commutatifs , Invent. Math. 101
1990
Cited alongside, same era.
Alain Connes and John Lott, Particle models and noncommutative geometry , Nuclear Phys. B Proc. Suppl. 18B
1990
Cited alongside, same era.
Lars Hörmander, An introduction to complex analysis in several variables , third ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR1045639 (91a:32001)
1990
Cited alongside, same era.
by same author, Critical points of Yang-Mills for noncommutative two-tori , J. Differential Geom. 31
1990
Cited alongside, same era.
Jerry L. Kazdan, Some applications of partial differential equations to problems in geometry , Tech. report, Tokyo University, 1983, originally part of the Surveys in Geometry series, available now in a revised edition, 1993, at http://www.math.upenn.edu/ ~
1993
Cited alongside, same era.
Ali H. Chamseddine and Alain Connes, The spectral action principle , Comm. Math. Phys. 186
1997
Cited alongside, same era.
Varghese Mathai and Jonathan Rosenberg, A noncommutative sigma-model , In preparation
Cited in the paper.
2003
Later among the works it cites.
Karlheinz Gröchenig and Michael Leinert, Wiener’s lemma for twisted convolution and Gabor frames , J. Amer. Math. Soc. 17
2004
Later among the works it cites.
A. Polishchuk, Classification of holomorphic vector bundles on noncommutative two-tori , Doc. Math. 9
2004
Later among the works it cites.
by same author, T T -duality for torus bundles with H H -fluxes via noncommutative topology , Comm. Math. Phys. 253
2005
Later among the works it cites.
Franz Luef, On spectral invariance of non-commutative tori , Operator theory, operator algebras, and applications, Contemp. Math., vol. 414, Amer. Math. Soc., Providence, RI, 2006, pp. 131–146. MR2277208
2006
Later among the works it cites.
by same author, T T -duality for torus bundles with H H -fluxes via noncommutative topology. II. The high-dimensional case and the T T -duality group , Adv. Theor. Math. Phys. 10
2006
Later among the works it cites.
Alexander Polishchuk, Analogues of the exponential map associated with complex structures on noncommutative two-tori , Pacific J. Math. 226
2006
Later among the works it cites.