基于下调和函数的“无平点”定理的群集简单模型中的“液-固”相变
A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions
摘要：
我们考虑了一个非局部形状最优化问题，这是由一个简单的模型的群集和其他自组装/聚集模型的动机，并证明了不同阶段的存在。证明了严格下调和函数在一个正测度集上不可能是常数。
英文摘要：
We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
