Determinante regularizado do Laplaciano e conjuntos isoespectrais em superfícies - Antas, Mateus da Silva Rodrigues (Universidade Federal de São Carlos, 2019)
On compact surfaces with boundary, with some conditions in a conformal class, we study the problem about to find a metric with constant Gaussian curvature with boundary of constant geodesic curvature for which the regularized determinant of Laplacian has a maximum. From this, we present applications to the problem to obtain a compact Riemannian manifold from its spectrum. Finally, we use the regularized determinant of Laplacian and the invariants of the heat kernel to study the compactness for isospectral sets of simply connected planar domains in a natural $C^{\infty}$ topology.
Regularized determinant of Laplacian and isospectral sets in surfaces
Keywords: Expansão assintótica do núcleo do calor; Métricas conformes; Conjuntos isoespectrais; Determinante regularizado do Laplaciano; Fórmula de Polyakov; Asymptotic expansion of the heat kernel; Conformal metrics; Isospectral sets; Regularized determinant of Laplacian; Polyakov formula; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA