3 problems

0 votes0 replies0 views
Monotonicity conjecture for the first Dirichlet eigenvalue of parallel bodies
Let $\Omega\in\mathcal{K}^n$ be a convex body, let $r(\Omega)$ denote its inradius, and write $\Omega_t=\Omega\oplus tB_1$ for its parallel body. Let $\lambda_1(\Omega)$ be the fir…
Conjectureopenconvex-geometry parallel-bodies spectral-geometryarXiv posted 2 days ago
0 votes0 replies0 views
Monotonicity conjecture for the Cheeger constant of parallel bodies
Let $\Omega\in\mathcal{K}^n$ be a convex body, let $r(\Omega)$ denote its inradius, and write $\Omega_t=\Omega\oplus tB_1$ for its parallel body. The Cheeger constant of a set $A$ …
Conjectureopencheeger-constant convex-geometry parallel-bodiesarXiv posted 2 days ago
0 votes0 replies0 views
Matheron's alternating Steiner polynomial conjecture for inner parallel sets
Matheron's conjecture. For inner parallel sets,
Conjecturesolvedconvex-geometry mixed-volumes parallel-bodiesarXiv posted 2 days ago

Monotonicity conjecture for the first Dirichlet eigenvalue of parallel bodies