All Questions

Let $f:\mathbb{R}^2 \to \mathbb{R}^2$ be a smooth map whose differential has fixed distinct singular values $0<\sigma_1<\sigma_2$ and an everywhere positive determinant (which is the product $\...

Let $(\mathcal{M},g)$ be a compact Riemannian manifold with Levi-Civita connection $\nabla$. It is well-known that the Poisson equation $$\Delta u=f$$ does have a solution on $C^{\infty}(\mathcal{M})$ ...

Can anyone think of a conformal Killing vector field $W$ on $S^2$ with the round metric that is not Killing such that its divergence is $L^2$-orthogonal to the spherical harmonics with $\ell = 1$? One ...