论文标题
Helfrich功能和应用的Li-Yau不平等现象
Li-Yau inequalities for the Helfrich functional and applications
论文作者
论文摘要
我们证明了helfrich功能的一般性不平等，其中自发曲率以奇异的体积类型积分进入。在身体相关的情况下，可以将该术语转换为明确的能量阈值，以保证嵌入。然后，我们将结果应用于各种坎am-helfrich模型的球形案例。如果最高能量不大，我们显示出平滑嵌入的最小化器的存在。以前，最小化的存在仅在浸入式气泡树或曲率的类别中已知。
We prove a general Li-Yau inequality for the Helfrich functional where the spontaneous curvature enters with a singular volume type integral. In the physically relevant cases, this term can be converted into an explicit energy threshold that guarantees embeddedness. We then apply our result to the spherical case of the variational Canham-Helfrich model. If the infimum energy is not too large, we show existence of smoothly embedded minimizers. Previously, existence of minimizers was only known in the classes of immersed bubble trees or curvature varifolds.
