Under sharp logarithmic lower bounds, solutions to the quasilinear Liouville equation on manifolds with nonnegative Ricci curvature force the manifold to be Euclidean with standard bubble solutions, plus finite-mass and volume-ratio results.
Brendle.Sobolev inequalities in manifolds with nonnegative curvature.Comm
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Quasilinear Liouville equation on manifolds with nonnegative Ricci curvature
Under sharp logarithmic lower bounds, solutions to the quasilinear Liouville equation on manifolds with nonnegative Ricci curvature force the manifold to be Euclidean with standard bubble solutions, plus finite-mass and volume-ratio results.