Local Rigidity of Teichm"uller space with Thurston metric
Local Rigidity of Teichm"uller space with Thurston metric
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具有Thurston度量的Teichm"uller空间的局部刚度
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通讯作者：
Huiping Pan
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作者：
Huiping Pan
我们证明，配备瑟斯顿范数的 Teichmuller 空间的余切空间之间的每个 $\mathbb R$-线性满射等距都是由底层双曲曲面之间的某种等距引起的，这类似于关于 Teichmuller 度量的 Royden 定理。由此，我们得到了瑟斯顿度量的局部刚性定理，以及由沃尔什首先证明的全局刚性定理的新证明。
We show that every $\mathbb R$-linear surjective isometry between the cotangent spaces to the Teichmuller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces, which is an analogue of Royden's theorem concerning the Teichmuller metric. Consequently, we obtain the local rigidity theorem of the Thurston metric, as well as a new proof of the global rigidity theorem which was first proved by Walsh.