3 problems

Does there exist a smooth embedded open annulus $S\subset\mathbb{R}^3$ with strictly negative Gaussian curvature and injective Gauss map $N:S\to\mathbb{S}^2$ that contains a simple…

Envelope characterization. The surface $\Phi$ contains the envelope of the family $C_t$ if and only if one of the following conditions holds:

Bloch-type conjecture. If this cup product map is zero, then the intersection product map