Browsing by Autor "Jean C. Cortissoz"

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    ON MARCH’S CRITERION FOR TRANSIENCE ON ROTATIONALLY SYMMETRIC MANIFOLDS
    (Cambridge University Press, 2025) John E. Bravo; Jean C. Cortissoz
    Abstract We show that March’s criterion for the existence of a bounded nonconstant harmonic function on a weak model (that is, $\mathbb {R}^n$ with a rotationally symmetric metric) is also a necessary and sufficient condition for the solvability of the Dirichlet problem at infinity on a family of metrics that generalise metrics with rotational symmetry on $\mathbb {R}^n$ . When the Dirichlet problem at infinity is not solvable, we prove some quantitative estimates on how fast a nonconstant harmonic function must grow.
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    Three-manifolds of positive curvature and convex weakly umbilic boundary
    (Springer Science+Business Media, 2008) Jean C. Cortissoz