论文标题
在非局部各向异性等激素问题中多型的最小
Minimality of polytopes in a nonlocal anisotropic isoperimetric problem
论文作者
论文摘要
我们考虑在体积约束下，通过晶体周长和Riesz类型的非局部相互作用给出的能量功能的最小化。我们表明，在小质量方案中，如果各向异性周边的wulff形状具有某些对称特性，那么它是总能量的独特全局最小化器。在尺寸二中，这适用于凸多边形，与角度相对于角度的反射对称。我们进一步证明了（局部）最小化器在两个维度上的结构是刚性的结果。
We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the anisotropic perimeter has certain symmetry properties, then it is the unique global minimizer of the total energy. In dimension two this applies to convex polygons which are reflection symmetric with respect to the bisectors of the angles. We further prove a rigidity result for the structure of (local) minimizers in two dimensions.
