arXiv subjects

Sergiu Moroianu

Publications and source records attributed to Sergiu Moroianu.

39 records · Page 3Linked to original sources

arXiv2004

On the $L^p$ index of spin Dirac operators on conical manifolds

We compute the index of the Dirac operator on spin Riemannian manifolds with conical singularities, acting from $L^p(Σ^+)$ to $L^q(Σ^-)$ with $p,q>1$. When $1+\frac{n}{p}-\frac{n}{q}>0$ we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at $\frac{n+1}{2}-\frac{n}{q}$ instead of 0 in the definition of the eta invariant. In particular we reprove Chou's formula for the $L^2$ index. For $1+\frac{n}{p}-\frac{n}{q}\leq 0$ the index formula contains an extra term related to the Calderón projector.

math.DG↗

arXiv2003

Weyl laws on open manifolds

Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume.

math.DG↗

arXiv2002

An index formula on manifolds with fibered cusp ends

We consider a compact manifold whose boundary is a locally trivial fiber bundle and an associated pseudodifferential algebra that models fibered cusps at infinity. Using trace-like functionals that generate the 0-dimensional Hochschild cohomology groups, we express the index of a fully elliptic fibered cusp operator as the sum of a local contribution from the interior and a term that comes from the boundary. This answers the index problem formulated by Mazzeo and Melrose. We give a more precise answer in the case where the base of the boundary fiber bundle is the circle. In particular, for Dirac operators associated to a "product fibered cusp metric", the index is given by the integral of the Atiyah-Singer form in the interior minus the adiabatic limit of the eta invariant of the restriction of the operator to the boundary.

math.DG↗