An a priori estimate for a fully nonlinear equation on four-manifolds

By S. Chang, M. Gursky, Paul Yang. 2002

175 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eb4a8138042a00f30a30556df7fb29bb1d1cf067

How researchers see this paper

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In Applied Mathematics

1. Yanyan Li
2. Neil S. Trudinger
3. Xu-jia Wang
4. Bo Guan
5. Weimin Sheng
6. Sophie Chen
7. M. Gursky
8. Jeff Viaclovsky

In Mathematical Physics

1. Yanyan Li
2. Neil S. Trudinger
3. Xu-jia Wang
4. M. Gursky
5. Paul Yang
6. Weimin Sheng
7. S. Chang
8. J. A. Gálvez

Citations in the corpus

• The inequality of Moser and Trudinger and applications to conformal geometry (2003, unknown): “In [12] we provide a priori estimates for solutions of the equation (3.”
• Local gradient estimates of solutions to some conformally invariant fully nonlinear equations (2006, background): “Fully nonlinear equations on Riemannian manifolds involving the Schouten tensor have been studied by Viaclovsky in [35] and [36], by Chang, Gursky and Yang in [4] and [3], and by many others; see for example [5], [22], [31], [37], and the references therein.”
• Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary (2006, unknown): “In [5,6], Chang et al.”
• Local estimates for some fully nonlinear elliptic equations (2005, background): “Local estimates are proved by Chang,Gursky, and Yang [2] (k = 2, l = 0 or 1, n = 4), Guan-Wang [7] (l = 0), and Guan-Wang [8] with the additional assumption (n − k + 1)(n − l + 1) > 2(n + 1).”
• Hypersurfaces in H n+1 and conformally invariant equations: the generalized Christoffel and Nirenberg problems (2007, background): “Such results by Li generalize other previous works, like [CGS, CGY2 , LL1, LL2].”
• The Yamabe problem for higher order curvatures (2005, methodology): “By Lemma 4.7, we can prove the existence of solutions of (2.1) by a degree argument, see [ CGY2 , LL1].”
• A class of fully nonlinear equations arising from conformal geometry (2006, background): “Chang, Gursky and Yang succeeded to solved the equation for σ2 in dimension 4 (see [4]).”
• Singular sets of a class of locally conformally flat manifolds (2005, unknown): “For instance, Chang-Gursky-Yang [4], [3], Gursky-Viaclovsky [12], Li-Li [14], Guan-Wang [11].”
• Recent developments in elliptic partial differential equations of Monge-Ampere type (2006, unknown): “1 are readily proven, [35], [13], [7], [14].”
• Remark on some conformally invariant integral equations: the method of moving spheres (2003, methodology): “ille type theorems have been extended to general conformally invariant fully nonlinear equations by Li and Li ([22]-[25]); see also related works of Viaclovsky ([35]-[36]) and Chang, Gursky and Yang ([11]-[12]). The method used in [19], as well as in much of the above cited work, is the method of mo”
• SECOND-ORDER ESTIMATES AND REGULARITY FOR FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS (2012, background): “[20], [29], and in conformal geometry in which there is a huge literature; see for instance [6], [7], [8], [12], [30], [31], [32], [33], [34], [40], [41], [42], [48], [53], [54] and references therein.”
• Prescribing symmetric functions of the eigenvalues of the Ricci tensor (2004, background): “results have managed to distinguish the case of the sphere, thereby giving bounds when the manifold is not conformally equivalent to S n . For example, [ CGY02a ]”