Some Remarks on the Prescribed Mean Curvature Equation on Complete Manifolds

@inproceedings{Pigola2002SomeRO,
  title={Some Remarks on the Prescribed Mean Curvature Equation on Complete Manifolds},
  author={Stefano Pigola and Marco Rigoli and Alberto G. Setti},
  year={2002}
}
  • Stefano Pigola, Marco Rigoli, Alberto G. Setti
  • Published 2002
Let (M, 〈, 〉) be a complete (noncompact), m-dimensional, m ≥ 2, Riemannian manifold and, for a fixed reference point o ∈ M , set r(x) = dist(M,〈,〉)(o, x). Thus BR and ∂BR denote, respectively, the geodesic ball and sphere of radius R centered at o. In what follows we shall always assume M connected. We associate to a smooth function u : M → R its graph Γu : M → M×R, defined by Γu : x → (x, u(x)). Indicating with (, ) the product metric on M × R, Γu : (M,Γu(, )) → (M × R, (, )) becomes an… CONTINUE READING