论文标题
在非紧凑类型的对称空间中的不稳定最小表面
Unstable minimal surfaces in symmetric spaces of non-compact type
论文作者
论文摘要
We prove that if $Σ$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $ρ:π_1(Σ)\to G$ and a $ρ$-equivariant unstable minimal map from the universal cover of $Σ$ to $N$.这是从高能量最小图指数上的新下限到非紧凑类型的任意对称空间的。服用$ g = \ mathrm {psl}（n，\ mathbb {r}）$，$ n \ geq 4 $，这反驳了labourie的猜想。
We prove that if $Σ$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $ρ:π_1(Σ)\to G$ and a $ρ$-equivariant unstable minimal map from the universal cover of $Σ$ to $N$. This follows from a new lower bound on the index of high energy minimal maps into an arbitrary symmetric space of non-compact type. Taking $G=\mathrm{PSL}(n,\mathbb{R})$, $n\geq 4$, this disproves the Labourie conjecture.
