All Questions
3 questions
7
votes
1
answer
716
views
A question on the Mahler conjecture
In its asymmetric version, the Mahler conjecture states that if $K \subset \mathbb{R^n}$ is a convex body containing the origin as an interior point and
$$
K^* := \{y \in \mathbb{R}^n : \langle y, x \...
3
votes
1
answer
444
views
Another diameter-perimeter-area inequality
Recently I learnt that $$\DeclareMathOperator{\diam}{diam}\DeclareMathOperator{\per}{per}\DeclareMathOperator{\area}{area}
\inf\frac{\diam(C)(\per(C)-2\diam(C))}{\area(C)}=0$$ where the infimum is ...
0
votes
2
answers
244
views
Decreasing magnitude of spherical centroid
Let $\sigma$ be the uniform measure on $\mathbb{S}^{d-1}\subset \mathbb{R}^d$. For any region $R\subset \mathbb{S}^{d-1}$, let $X_R$ be a random variable which is uniformly distributed across $R$. We ...