论文标题
固定平面p-弹性
Pinned planar p-elasticae
论文作者
论文摘要
在我们以前的工作的基础上，我们将所有平面$ p $ - 弹性机分类为固定的边界条件，然后获得全球最小化器的独特性和几何特性。作为一个应用程序，我们为$ p $ bendend Energy建立了li-Yau类型不平等，特别是发现独特的指数$ p \ simeq 1.5728 $，以实现全部优化。我们还证明存在最小的$ p $弹性网络，从而扩展了Dall'acqua-Novaga-Pluda的最新结果。
Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda.
