Maximal estimates for Schrödinger means and convergence almost everywhere of sequences are studied.

We prove that the Weinstock inequality for first nonzero Steklov eigenvalue holds in $\mathbb{R}^n$, $n \geq 3$, class of convex sets with prescribed surface area. The key result is a sharp isoperimetric involving simultaneously area, volume and boundary momentum sets. As by-product, we also obtain some inequalities Wentzell eigenvalue.

We show that ( n + 1)-dimensional Myers–Perry metrics, ≥ 4, have a conformal completion at space-like infinity of C n−3,1 differentiability class and the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.

Let $$p\in {\mathbb {Z}}^n$$ be a primitive vector and $$\Psi :{\mathbb {Z}}^n\rightarrow {Z}}, z\rightarrow \min (p\cdot z, 0)$$ . The theory of husking allows us to prove that there exists pointwise minimal function among all integer-valued superharmonic functions equal $$ “at infinity”. We apply this result sandpile models on $${\mathbb existence so-called solitons in model, discovered 2-dim...