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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
43/2005

Conformal deformations of the smallest eigenvalue of the Ricci tensor

Pengfei Guan and Guofang Wang

Abstract

We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor to be a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest eigenvalue of the Ricci tensor to be a constant is an extremal metric of volume in a suitable sense in the conformal class. The problem is reduced to solve a Pucci type equation with respect to the Schouten tensor. We establish a local gradient estimate for this type of conformally invariant fully nonlinear uniform elliptic equations. Combining it with the theory of fully nonlinear equations, we establish the existence of solutions for this equation.

Received:
May 5, 2005
Published:
May 5, 2005
MSC Codes:
53C21, 35J6, 58E11
Keywords:
conformal deformation, ricci tensor, minimal volume, fully nonlinear equation, local estimates

Related publications

inJournal
2007 Repository Open Access
Pengfei Guan and Guofang Wang

Conformal deformations of the smallest eigenvalue of the Ricci tensor

In: American journal of mathematics, 129 (2007) 2, pp. 499-526