All Questions

The $2$-sphere $S^2$ endowed with usual round metric, we have a Laplacian operator $\Delta_{\mathrm{d}} = \mathrm{d}^*\mathrm{d} + \mathrm{d}\mathrm{d}^*$ acting on functions. The eigenvalues of this ...

For a (compact) spin manifold, we know that the eigenvalues $\lambda_n$ of the Dirac operator are countable, with finite multiplicity, and satisfy $$ |\lambda_n| \to \infty, ~~~ \text{ as } n \to \...

For a Kahler manifold $M$, let us denote its Dirac operator $\overline{\partial} + \overline{\partial}^\ast$, with respect to a metric $g$, by $D$. Moreover, let us dentoe the Levi-Civita connection ...

This is a question for all you number theorists out there...based on my skimming of number theory textbooks and survey articles, it seems like most of the applications of geometry and complex ...