Journal ArticleDOI
A perturbation result in prescribing scalar curvature on Sn
Sun-Yung Alice Chang,Paul Yang +1 more
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This article is published in Duke Mathematical Journal.The article was published on 1991-10-01. It has received 221 citations till now. The article focuses on the topics: Scalar curvature & Prescribed scalar curvature problem.read more
Citations
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Harnack type inequality : the method of moving planes
TL;DR: In this article, a Harnack type inequality is established for solutions to some semilinear elliptic equations in dimension two, which originated from some Chern-Simons Higgs model.
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The scalar curvature equation on 2- and 3-spheres
TL;DR: In this paper, the authors obtained a priori estimates for solutions to the prescribed scalar curvature equation on 2-and 3-spheres under a nondegeneracy assumption on the curvature function.
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Extremal metrics of zeta function determinants on 4-manifolds
Sun-Yung Alice Chang,Paul Yang +1 more
TL;DR: In conformal geometry, the Sobolev inequality at a critical exponent has received much attention as mentioned in this paper, and the determination of the best constants has played a crucial role in the Yamabe problem.
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On a fractional Nirenberg problem, part I: Blow up analysis and compactness of solutions
TL;DR: In this paper, the existence and compactness of fractional Nirenberg problems were proved. But the authors did not prove the existence of a compact solution of the fractional nirenberg problem.
Prescribing scalar curvature on Sn and related problems
TL;DR: In this article, Nirenberg posed the question: quelles fonctions K(x) sur S 2 peuvent representer la Courbure de Gauss d'une metrique g sur S n, qui est conformement equivalent a g 0?
References
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A relation between pointwise convergence of functions and convergence of functionals
TL;DR: In this article, it was shown that if f n is a sequence of uniformly L p-bounded functions on a measure space, and f n → f pointwise a, then lim for all 0 < p < ∞.
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Best constant in Sobolev inequality
TL;DR: The best constant for the simplest Sobolev inequality was proved in this paper by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus of variations.
Book
Topics in Nonlinear Functional Analysis
TL;DR: Topological approach: Finite dimensions Topological degree in Banach space Bifurcation theory Further topological methods Monotone operators and the min-max theorem Generalized implicit function theorems Bibliography as mentioned in this paper
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Extremals of determinants of Laplacians
TL;DR: On etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand the metrique est bien restreinte.