6 problems

For each integer $n\geq 3$, let $\gamma_n(t)=(t,t^2,\ldots,t^n)$ be the moment curve in $\mathbb{R}^n$, equipped with the associated nonisotropic dilations and Hardy space…

Almost rectangular cap characterization conjecture. The almost rectangular caps of ${\mathbb M}$, and hence of ${\mathfrak M}$, are characterized by condition in Lemma.

For integers $n\geq 2$, parameters $0\leq \beta\leq n-1$, and $s\geq 1$, let $e(t)=e^{2\pi i t}$ and integrate over $[0,1]^{n-1}\times[0,N^{-\beta}]$. Mean value conjecture for the…

For integers $k,n$ with $k>3$, let $\mathcal{A}_{k,n}$ denote the Minkowski sum of $n$ copies of the moment-curve segment $\{(t,t^2,\ldots,t^k)\mid -1\leq t\leq 1\}$. Unique bounda…

For integers $k,n$ with $k>3$, let $\mathcal{A}_{k,n}$ denote the Minkowski sum of $n$ copies of the moment-curve segment $\{(t,t^2,\ldots,t^k)\mid -1\leq t\leq 1\}$. Let…

Conjectural formula. For even $k$, the value of $\phi_k$ satisfies