论文标题
Fuchsian DPW的Lawson表面潜力
Fuchsian DPW potentials for Lawson surfaces
论文作者
论文摘要
lawson表面$ξ_{1，g} $ g $的$是通过旋转和反映高原解决方案$ f_t $相对于特定的地理$ 4 $ -4 $ -GON $ -GON $γ_T$，其中$ t = \ t = \ tfrac {1}} {1} {2G+2} $是$γ__的角度。在本文中，我们将高原解决方案的存在和规律性结合在$ t \ in（0，\ tfrac {1} {4}）中的$ f_t $与有关fuchsian Specter of 4-puncture Sphere上的模态空间的拓扑信息，以获得A Fuchsian Dpw潜在的$η_t$的存在\ tfrac {1} {4} $。这导致了一种算法，可以共同参数所有Lawson表面$ξ_{1，G} $。
The Lawson surfaces $ξ_{1,g}$ of genus $g$ are constructed by rotating and reflecting the Plateau solution $f_t$ with respect to a particular geodesic $4$-gon $Γ_t$ along its boundary, where $t= \tfrac{1}{2g+2}$ is an angle of $Γ_t$. In this paper we combine the existence and regularity of the Plateau solution $f_t$ in $t \in (0, \tfrac{1}{4})$ with topological information about the moduli space of Fuchsian systems on the 4-puncture sphere to obtain existence of a Fuchsian DPW potential $η_t$ for every $f_t$ with $t\in(0, \tfrac{1}{4}]$. Moreover, the coefficients of $η_t$ are shown to depend real analytically on $t$. This implies that the Taylor approximation of the DPW potential $η_t$ and of the area obtained at $t=0$ found in \cite{HHT2} determines these quantities for all $ξ_{1,g}$. In particular, this leads to an algorithm to conformally parametrize all Lawson surfaces $ξ_{1,g}$.
