Infinite dimensionality of kernels of Neumann Laplacians induced by first-order elliptic operators

31.01.2019, 16:15  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Lashi Bandara

We consider first-order elliptic differential operators on a compact manifold with boundary. We show that the kernel of the maximal extension, which coincides with the kernel of its associated Neumann Laplacian, is infinite dimensional. These results are obtained by first-order methods, index theory, and through the use of the existence of generalised Atiyah-Patodi-Singer boundary conditions with increasing dimension.