Isoperimetry in Surfaces of Revolution with Density
Isoperimetry in Surfaces of Revolution with Density
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DOI：
10.35834/mjms/1544151692
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发表时间：
2017-09
影响因子：
0.4
通讯作者：
Eliot Bongiovanni;Alejandro Diaz;Arjun Kakkar;Nat Sothanaphan
中科院分区：
文献类型：
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作者：
Eliot Bongiovanni;Alejandro Diaz;Arjun Kakkar;Nat Sothanaphan
具有密度或加权的等周问题寻求用最小加权周长包围规定的加权体积。根据钱伯斯最近对对数凸密度猜想的证明，对于$\mathbb{R}^n$上的许多密度，答案是关于原点的球面。我们试图将他的结果推广到其他一些空间的革命或两个不同的密度的体积和周长。我们提供了一般结果的存在性和有界性和一个新的方法来证明圆的起源等周。
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on $\mathbb{R}^n$ the answer is a sphere about the origin. We seek to generalize his results to some other spaces of revolution or to two different densities for volume and perimeter. We provide general results on existence and boundedness and a new approach to proving circles about the origin isoperimetric.