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Calculus of Variations

- S. Brendle, Jeff A. Viaclovsky
- Nature

Prof. FORSYTH'S latest work appears opportunely at a time when there is quite a notable revival of interest in the calculus of variations. To those who desire an account of the subject which, while… Expand

Conformal geometry, contact geometry, and the calculus of variations

- Jeff A. Viaclovsky
- Mathematics
- 1 February 2000

for metricsg in the conformal class of g0, where we use the metric g to view the tensor as an endomorphism of the tangent bundle and where σk d notes the trace of the induced map on the kth exterior… Expand

Estimates and Existence Results for some Fully Nonlinear Elliptic Equations on Riemannian Manifolds

- Jeff A. Viaclovsky
- Mathematics
- 24 April 2001

We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.

Fully nonlinear equations on Riemannian manifolds with negative curvature

- M. Gursky, Jeff A. Viaclovsky
- Mathematics
- 18 October 2002

We consider the problem of conformally deforming a metric to one with a prescribed symmetric function of the eigenvalues of the Ricci tensor, in the case of negative curvature.

A Fully Nonlinear Equation on Four-Manifolds with Positive Scalar Curvature

- M. Gursky, Jeff A. Viaclovsky
- Mathematics
- 30 January 2003

We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform… Expand

Prescribing symmetric functions of the eigenvalues of the Ricci tensor

- M. Gursky, Jeff A. Viaclovsky
- Mathematics
- 10 September 2004

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… Expand

Bach-flat asymptotically locally Euclidean metrics

- G. Tian, Jeff A. Viaclovsky
- Mathematics
- 19 October 2003

We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kähler… Expand

Some properties of the Schouten tensor and applications to conformal geometry

- Pengfei Guan, Jeff A. Viaclovsky, Guofang Wang
- Mathematics
- 14 March 2002

The Riemannian curvature tensor decomposes into a conformally invariant part, the Weyl tensor, and a non-conformally invariant part, the Schouten tensor. A study of the kth elementary symmetric… Expand

Moduli spaces of critical Riemannian metrics in dimension four

- Jeff A. Viaclovsky, G. Tian
- Mathematics
- 16 December 2003

Abstract We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar… Expand

Volume growth, curvature decay, and critical metrics

- Jeff A. Viaclovsky, G. Tian
- Mathematics
- 17 December 2006

We make some improvements to our previous results in [TV05a] and [TV05b]. First, we prove a version of our volume growth theorem which does not require any assumption on the first Betti number.… Expand

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