3 problems

Crossover conjecture. As the size of $r$ is increased, the asymptotic value of $\gamma$ for $\Delta r\gg 1$ should shift downward from

Let $S$ be a smooth compact surface in $\mathbb{R}^3$ with positive definite second fundamental form, and let $d\sigma$ be its induced Lebesgue measure. Define the Fourier extensio…

The paper considers a particle constrained to a two-dimensional curved surface and obtains the geometric potential by enlarging and constructing quantum conditions involving positi…