当前位置: X-MOL 学术Ann. Glob. Anal. Geom. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A rigidity theorem for ideal surfaces with flat boundary
Annals of Global Analysis and Geometry ( IF 0.7 ) Pub Date : 2019-08-31 , DOI: 10.1007/s10455-019-09685-6
James McCoy , Glen Wheeler

We consider surfaces with boundary satisfying a sixth-order nonlinear elliptic partial differential equation corresponding to extremising the $$L^2$$ L 2 -norm of the gradient of the mean curvature. We show that such surfaces with small $$L^2$$ L 2 -norm of the second fundamental form and satisfying so-called flat boundary conditions are necessarily planar.

中文翻译:

具有平坦边界的理想曲面的刚性定理

我们考虑具有满足六阶非线性椭圆偏微分方程的边界的曲面,该方程对应于平均曲率梯度的极值$$L^2$$L 2 -范数。我们表明,具有第二基本形式的小 $$L^2$$L 2 -范数并满足所谓的平坦边界条件的表面必然是平面的。
更新日期:2019-08-31
down
wechat
bug