Dominique Hulin

Prescribing curvature on open surfaces

In this article, we study the problem (sometimes called the Berger-Nirenberg problem) of prescribing the curvature on a Riemann surface (that is on an oriented surface equipped with a conformal class of Riemannian metrics).

Kahler-Einstein metrics and projective embeddings

We prove that the complex projective space equipped with its Fubini-Study metric admits no compact Kähler-Einstein submanifold with nonpositive Einstein constant. In particular, the Calabi-Yau metrics carried by an algebraic K3 surface cannot be realized by projective embeddings.

Mean Curvature and Asymptotic Volume of Small Balls

Marin Mersenne (1588–1648) is remembered chieflyasaone-man scientific clearing house—the Internet of his day. During the first half of theseventeenth century, when mathematical physics was taking its first tentative stepsguided by Descartes and Galileo, “Mersenne did more to propagate emerging newsciences of acoustics, pneumatics, and ballistics than anyone else of his time” [

Analysis on Riemannian manifolds and Ricci curvature

Analysis on Riemannian manifolds stems from the following simple fact: the classical Laplace operator has an exact Riemannian analog. Indeed, the properties of the Laplacian on a bounded Euclidean domain and on a compact Riemannian manifold are very similar, and so are the proofs. It can be said that the difficulties of the latter case, compared with the former, are essentially conceptual.