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The role of the curvature of a surface in the shape of the solutions to elliptic equations
We prove uniqueness and non-degeneracy of the critical point of positive, semi-stable solutions of $-Δu=f(u)$ with Dirichlet boundary conditions for a class of star-shaped domains of the sphere and of the hyperbolic plane satisfying a geometric condition. In the spherical case, this condition is wea
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