7 problems

Positive boundedness conjecture. Every such datum $\mathbf{H}_\mathbf{M}$ is $\mathbf{p}$-bounded.

B-conjecture. The following inequality holds:

Let $(\mathcal{A},w)$ be the input datum, let $\delta$ be the parameter defining the initialization region $D_\delta$, and let $c$ be the parameter in Theorem 5.1 that appears in t…

For each $1\leq j\leq m$, let $\Sigma_j:U_j\to\mathbb{R}^n$ be a smooth parametrization of an $n_j$-dimensional submanifold $S_j$ by a neighborhood $U_j$ of the origin in…

Let $V$ be a manifold and let $\Gamma_1,\dots,\Gamma_n$ be a transverse family of good fibrations of $V$, with corresponding maps $\pi_j:V\to U_j$ and forms $\omega_j$. For each…

Let $f$ be an even probability density on $\mathbb{R}$ with variance $1$, and let … be the standard normal density. Let $\mu$ be an even isotropic measure on $S^{n-1}$ supported at…

Let $U_j$ be compact neighbourhoods of the origin in $\mathbb{R}^{d-1}$, let $\Sigma_j:U_j\to\mathbb{R}^d$ be $C^{1,\beta}$ parametrisations of codimension-one submanifolds $S_j$,…