Prescribing symmetric functions of the eigenvalues of the Ricci tensor

By M. Gursky, Jeff Viaclovsky. 2004

144 citations recorded by the source corpus.

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/af69e34130d1453e5bd009376f1a3a70641c9478

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In Applied Mathematics

1. Bo Guan
2. Neil S. Trudinger
3. Xinan Ma
4. Guohuan Qiu
5. Xu-jia Wang
6. Weimin Sheng
7. H. Jiao
8. Robert J. McCann

In Astronomy and Astrophysics

1. Xinan Ma
2. Guohuan Qiu
3. Weimin Sheng
4. Xu-jia Wang
5. Neil S. Trudinger
6. Bo Guan
7. Pengfei Guan

Citations in the corpus

• 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.”
• On Harnack inequalities and singularities of admissible metrics in the Yamabe problem (2005, methodology): “9) is the k-Yamabe problem, which has been studied by many authors; see [1,22,26] for k = 1 and [5,6,10,14, 18,20,21,24,29] for k ≥ 2.”
• The Neumann Problem for Hessian Equations (2015, methodology): “Y.Li [22], Urbas [44] and Guan [13]. In recent years the Hessian type equation also appears in conformal geometry, which started from Chang-Gursky-Yang [5] and the related development by ([16], [23], [17], [36],[10]). In Kahler geometry, the Hessian equation was studied by Hou-Ma-Wu [18] and Dinew-K”
• The Yamabe problem for higher order curvatures (2005, background): “Very recently Gursky and Viaclovsky [ GV2 ] solved the problem for k > n 2, using the”
• Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds (2014, background): “= ψ(x)e (where Sg is the Schouten tensor of (M , g)) introduced by Viaclovsky [50] is connected with a natural fully nonlinear version of the Yamabe problem and has very interesting applications in conformal geometry; see for instance [5], [10], [26], [28], [35], [43] and references therein.”