Abstract

We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor is 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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 499-526
Launched on MUSE
2007-04-05
Open Access
No
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