论文标题
涉及平面凸的脸颊常数的尖锐不平等现象
Sharp inequalities involving the Cheeger constant of planar convex sets
论文作者
论文摘要
我们有兴趣通过不同的几何数量找到Cheeger常数$ h $的尖锐界限，即面积$ | \ cdot | $，外围$ p $，inradius $ r $，the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the the diameter $ d $ d $。我们为平面凸体的这些数量之间提供了新的尖锐不平等，并根据数值模拟发出了新的猜想。特别是，我们完全解决了blaschke-santaló图，描述了涉及三胞胎$（p，p，h，r）$，$（d，h，h，r）$和$（r，h，h，r）$的所有可能的不平等，并描述了三胞胎图的某些部分的界限，并描述了三胞胎图的某些部分$（ω，h，| \ cdot |）$，$（r，h，d）$和$（ω，h，r）$。
We are interested in finding sharp bounds for the Cheeger constant $h$ via different geometrical quantities, namely the area $|\cdot|$, the perimeter $P$, the inradius $r$, the circumradius $R$, the minimal width $ω$ and the diameter $d$. We provide new sharp inequalities between these quantities for planar convex bodies and enounce new conjectures based on numerical simulations. In particular, we completely solve the Blaschke-Santaló diagrams describing all the possible inequalities involving the triplets $(P,h,r)$, $(d,h,r)$ and $(R,h,r)$ and describe some parts of the boundaries of the diagrams of the triplets $(ω,h,d)$, $(ω,h,R)$, $(ω,h,P)$, $(ω,h,|\cdot|)$, $(R,h,d)$ and $(ω,h,r)$.
