All Questions

Hodge theory for elliptic complexes $E$ identifies the space of harmonic sections with cohomology $$\mathcal{H}(E) \simeq H(E).$$ A classical example with differential forms ($E = (\Omega,d)$) ...

Let $X$ be a complete Riemannian manifold and $H$ be the kernel of generalized Dirac operator $D$ on $L(S)$, where $S$ is the Dirac bundle. Let $K$ be a compact subset of $X$ and $K\subset \Omega$ be ...

Let $(M,g)$ be a complete Riemannian manifold, $\Delta$ its Laplace-Beltrami operator and $T_t = (e^{t \Delta})_{t \geq 0}$ the associated heat semigroup. We can define the subordinated Poisson ...

Let $D$ be a generalized Dirac operator on a complete Riemannian manifold. I'm a little confused to prove that there exists a constant $c>0$ such that $$\|D\sigma\|^2\geq c^2\|\sigma\|^2$$ for $\...