Curvature Functions for Compact 2-Manifolds

@article{Kazdan1974CurvatureFF,
  title={Curvature Functions for Compact 2-Manifolds},
  author={Jerry Kazdan and Frank W. Warner},
  journal={Annals of Mathematics},
  year={1974},
  volume={99},
  pages={14}
}
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501 Citations
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152
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70
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501 Citations

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References

SHOWING 1-10 OF 43 REFERENCES
On Imbeddings into Orlicz Spaces and Some Applications
A sharp form of an inequality by N
  • Trudinger, Indiana U. Math. J. 20
  • 1971
An application of generalized degree to a class of nonlinear problems
  • Troisieme Colloq. Analyse Fonctionelle, Liege, Sept. 1970, Centre Belge De Rech. Math. Vander
  • 1971
Œuvres de Charles Hermite: Sur la fonction exponentielle
Partial differential equations
Many physical problems involve quantities that depend on more than one variable. The temperature within a “large”1 solid body of conducting material varies with both time and location within the…
SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS
On a Nonlinear Problem in Differential Geometry
Conformal Metrics in R^2 with Prescribed Curvature
On the Conformal Equivalence of Compact 2-Dimensional Manifolds
The Generalized Minkowski Problem in Differential Geometry in the Large
...
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