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math.DG2023★ 5 cited
On the fundamental tone of the -Laplacian on Riemannian manifolds and applications
Francisco G. de S. Carvalho, Marcos Petrucio Cavalcante
We present a general lower bound for the fundamental tone for the -Laplacian on Riemannian manifolds carrying a special kind of function. We then apply our result to the cases o…
math.DG2023
Index bounds for closed minimal surfaces in 3-manifolds with the Killing property
Marcos P. Cavalcante, Darlan F. de Oliveira, Robson dos S. Silva
Let be a closed minimal surface immersed in a Riemannian 3-manifold carrying an orthonormal Killing frame. This class of ambient spaces includes Lie groups with a bi-invariant…