The dimension of the moduli space of superminimal surfaces of a fixed degree and conformal structure in the 4-sphere

スポンサーリンク

概要

• 論文の詳細を見る

• It was established by X. Mo and the author that the dimension of each irreducible component of the moduli space $\mathcal{M} <d,g>(X)$ of branched superminimal immersions of degree $d$ from a Riemann surface $X$ of genus $g$ into $\textbf{\textit{C}}P^3$ lay between $2d-4g+4$ and $2d-g+4$ for $d$ sufficiently large, where the upper bound was always assumed by the irreducible component of totally geodesic branched superminimal immersions and the lower bound was assumed by all nontotally geodesic irreducible components of $\mathcal{M} <6,1>(T)$ for any torus $T$. It is shown, via deformation theory, in this note that for $d=8g+1+3k$, $k\geq 0$, and any Riemann surface $X$ of $g\geq 1$, the above lower bound is assumed by at least one irreducible component of $\mathcal{M} <d,g>(X)$.

• 東北大学の論文

著者

• Chi Quo-shin

  Department Of Mathematics Washington University

関連論文

• Rigidity of superminimal surfaces in complex projective spaces
• The dimension of the moduli space of superminimal surfaces of a fixed degree and conformal structure in the 4-sphere
• Normalized potentials of minimal surfaces in spheres
• Rigidity of superminimal immersions of compact Riemann surfaces into CP^2

スポンサーリンク