Mathematics Problem Archive

Given a polygonal room with perfectly reflecting sides and a point light source, characterize when every point of the room is illuminated. In particul...

Consider minimal immersions $S^n\to S^N(1)$ with total area at most a fixed constant $A$, identifying immersions which differ by a motion of the ambie...

Let $B$ be a set of $n+2$ hyperplanes in general position in complex projective space $\mathbb{P}^n(\mathbb{C})$. Prove that there is no nondegenerate...

Let $\Delta$ be a ball in $\mathbb{C}^n$, $n\geq2$, and let $F$ be a complete Hermitian manifold. Does every holomorphic map from $\Delta\setminus\{0\...

Are there any complete surfaces of negative curvature in Euclidean 3-space whose principal curvatures are bounded away from zero?...