6 papers
Hadamard-type variation formulae for the eigenvalues of a class of second-order elliptic operators and its applications
Cleiton Lira Cunha, José Nazareno Vieira Gomes, Marcus Antônio Mendonça Marrocos
We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold . We then apply the latter in t…
On a special class of gradient Ricci solitons
José Nazareno Vieira Gomes, Marcus Antonio Mendonça Marrocos
We develop a method for constructing complete gradient Ricci solitons realized as fiber bundles endowed with warped metrics, and we establish necessary and sufficient conditions fo…
Asymptotic Analysis of Laplacian Operator in Thin Domains on the Sphere with Highly Oscillatory Boundary
NaÃsa C. Garcia, Raquel Lehrer, Marcus A. M. Marrocos
In this work we analyse the convergence of solutions of the Poisson equation with Neumann boundary conditions in a thin domain with highly oscillatory behavior $\mathcal{U}^\vareps…
On the generic Simplicity of the spectrum for Connection Laplacian and -simplicity on Principal Bundles
Geovane C. Brito, Marcus A. M. Marrocos
In this paper, we prove that, for a residual set of connections defined on a smooth vector bundle , all eigenvalues of the connection Laplacian operator $\mathscr{…
Hidden symmetries and the generic spectral setting of generalized laplacians on homogeneous spaces
Diego S. De Oliveira, Marcus A. M. Marrocos
The purpose of this work is to establish the spectral setting of some generalized Laplace operators associated to a generic -invariant metric on a compact homogeneous space $M=G…
A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces
Diego S. de Oliveira, Marcus A. M. Marrocos
Petrecca and Röser (2018, \cite{Petrecca2019}), and Schueth (2017, \cite{Schueth2017}) had shown that for a generic -invariant metric on certain compact homogeneous spaces…