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Some Nonlinear Problems in Riemannian Geometry

- Thierry Aubin
- Materials Science, Mathematics
- 31 July 1998

1 Riemannian Geometry.- 2 Sobolev Spaces.- 3 Background Material.- 4 Complementary Material.- 5 The Yamabe Problem.- 6 Prescribed Scalar Curvature.- 7 Einstein-Kahler Metrics.- 8 Monge-Ampere… Expand

Nonlinear analysis on manifolds, Monge-Ampère equations

- Thierry Aubin
- Mathematics
- 1982

1 Riemannian Geometry.- 1. Introduction to Differential Geometry.- 1.1 Tangent Space.- 1.2 Connection.- 1.3 Curvature.- 2. Riemannian Manifold.- 2.1 Metric Space.- 2.2 Riemannian Connection.- 2.3… Expand

The Ricci Curvature

- Thierry Aubin
- Physics
- 1998

In this chapter we deal with problems concerning Ricci Curvature mainly:
Prescribing the Ricci curvature
Ricci curvature with a given sign
Existence of Einstein metrics.

The Scalar Curvature

- Thierry Aubin
- Mathematics
- 1976

We shall deal with some problems concerning the scalar curvature of compact riemannian manifolds. In particular we shall deal with the problem of Yamabe: Does there exist a conformal metric for which… Expand

On the best Sobolev inequality

- Thierry Aubin, Yanyan Li
- Mathematics
- 1 April 1999

Abstract We prove that the best constant in the Sobolev inequality ( W 1 , P ⊂ L p* with 1/ p * = 1/ p − 1/ n and 1 p n ) is achieved on compact Riemannian manifolds, or only complete under some… Expand

Best constants in Sobolev inequalities for compact manifolds of nonpositive curvature

- Thierry Aubin, Olivier Druet, Emmanuel Hebey
- Mathematics
- 1 May 1998

Abstract Let (M,g) be a smooth compact Riemannian n-manifold, n ≥ 2, let p(1, n) real, and let H1p (M) be the standard Sobolev space of order p. By the Sobolev embedding theorem, H1p(M) ⊂ Lp* (M)… Expand

A course in differential geometry

- Thierry Aubin
- Mathematics
- 12 December 2000

Background material Differentiable manifolds Tangent space Integration of vector fields and differential forms Linear connections Riemannian manifolds The Yamabe problem-An introduction to research… Expand

BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM

- Thierry Aubin
- Mathematics
- 31 January 1982

The Mass according to Arnowitt, Deser and Misner

- Thierry Aubin
- Mathematics
- 15 July 2007

Abstract For asymptotically Euclidean manifolds of order τ > ( n − 2 ) / 2 , under the hypothesis that the mass m (according to Arnowitt, Deser and Misner) exists (in particular if the scalar… Expand

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