All Questions

This is a cross-post from MSE (no answer there). Let $M,N$ be oriented $d$-dimensional Riemannian manifolds, $M$ compact*, and let $f:M \to N$ be smooth. Consider the Dirichlet energy functional: $...

This is a cross-post from MSE (where I got no answer). It is well-known that conformal maps between $2$-dimensional Riemannian manifolds are harmonic. I discovered lately that in dimension $d>2$, ...

Consider a compact surface $M$ of genus $g \geq 2$ with a metric of constant negative curvature. My question is, is it known under what sorts of sufficient conditions such a metric will have non-...

Recently, Andrews and Li announced a complete classification of CMC ($H=const.$) tori in $S^3$, confirming a conjecture of Pinkall and Sterling. Their main result is that any such torus is ...