In this talk I will describe some gap estimates for ’even’ and self-dual AHE metrics in dimension four. Even AHE metrics naturally arise from a non-local variational problem, and there is an interesti...
The volume entropy is a fundamental geometric invariant defined as the exponential growth rate of volumes of balls in the universal cover. It is a very subtle invariant which has attracted extensive s...
It is a jointwork with I. Mondello (Creteil) and D. Tewodrose (Bruxelles). J. Cheeger and A. Naber have shown that if \((X, d)\) is a Gromov-Hausdorff limit of a sequence of complete Riemannian manifo...
I will first discuss the pioneering work of Hsiang and Hsiang–Lawson on the construction of minimal sub-manifolds using equivariant geometry, and then some extensions of their theory including new exi...
We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic type and derive a co...
With Alix Deruelle, we explain how Ricci flow develops or resolves 4-dimensional orbifold singularities by a notion of stability depending only on the curvature at the singular points. We construct a ...
The concept of mass for time-symmetric initial data has been extensively explored and is now a cornerstone in the study of contemporary Mathematical General Relativity, especially in relation to space...
We will consider the classical problem, proposed by Kazdan and Warner in the 70’s, of prescribing the scalar curvature of a Riemannian manifold via conformal deformations of the metric. This amounts t...
We will consider the classical problem, proposed by Kazdan and Warner in the 70’s, of prescribing the scalar curvature of a Riemannian manifold via conformal deformations of the metric. This amounts t...
We will consider the classical problem, proposed by Kazdan and Warner in the 70’s, of prescribing the scalar curvature of a Riemannian manifold via conformal deformations of the metric. This amounts t...
