Hadamard-type variation formulae for the eigenvalues of a class of second-order elliptic operators and its applications
Year: 2026
Type: article
Abstract: We use variational methods to derive Hadamard-type formulae for the eigenvalues of a class of elliptic operators on a compact Riemannian manifold M . We then apply the latter in the following context. Consider a family of elliptic operators which is parametrized by either the set of all $$\mathcal {C}^r$$ C r –Riemannian metrics on M or the set of all $$\mathcal {C}^r$$ C r –diffeomorphisms on a domain into M . In either case, we prove that if a subset of the parametrizations set yields a simple spectrum of the operator, then it is necessarily a generic subset. We also analyse the behavior of the eigenvalues when the metric evolves along the Ricci flow on a closed Riemannian manifold, and we prove, under a suitable hypothesis, that they increase.
Authors: C. L. Cunha, J. N. V. Gomes, M. A. M. Marrocos
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4380551880