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1. CJM 2000 (vol 52 pp. 757)

Hanani, Abdellah
Le problème de Neumann pour certaines équations du type de Monge-Ampère sur une variété riemannienne
Let $(M_n,g)$ be a strictly convex riemannian manifold with $C^{\infty}$ boundary. We prove the existence\break of classical solution for the nonlinear elliptic partial differential equation of Monge-Amp\`ere:\break $\det (-u\delta^i_j + \nabla^i_ju) = F(x,\nabla u;u)$ in $M$ with a Neumann condition on the boundary of the form $\frac{\partial u}{\partial \nu} = \varphi (x,u)$, where $F \in C^{\infty} (TM \times \bbR)$ is an everywhere strictly positive function satisfying some assumptions, $\nu$ stands for the unit normal vector field and $\varphi \in C^{\infty} (\partial M \times \bbR)$ is a non-decreasing function in $u$.

Keywords:connexion de Levi-Civita, équations de Monge-Ampère, problème de Neumann, estimées a priori, méthode de continuité
Categories:35J60, 53C55, 58G30

2. CJM 1997 (vol 49 pp. 359)

Sawyer, P.
Estimates for the heat kernel on $\SL (n,{\bf R})/\SO (n)$
In \cite{Anker}, Jean-Philippe Anker conjectures an upper bound for the heat kernel of a symmetric space of noncompact type. We show in this paper that his prediction is verified for the space of positive definite $n\times n$ real matrices.

Categories:58G30, 53C35, 58G11

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