论文标题
各向异性最小理论：各向异性最小和CMC表面的存在
The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces
论文作者
论文摘要
我们证明存在具有恒定各向异性平均曲率的非平凡闭合表面，相对于椭圆形的封闭平滑$ 3 $维的riemannian歧管。构造的最小最大表面是光滑的，最多有一个单数点。恒定各向异性平均曲率可以固定为任何实际数字。特别是，我们部分解决了Allard [Invent。 Math。，1983]尺寸$ 3 $。
We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth $3$-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension $3$.
