论文标题
退化Riemann-Hilbert-Birkhoff问题，半透明性和WDVV电位的收敛性
Degenerate Riemann-Hilbert-Birkhoff problems, semisimplicity, and convergence of WDVV-potentials
论文作者
论文摘要
在本文的第一部分中，我们提供了C. sabbah定理的新分析证明，内容涉及$ \ Mathbb p^1 $在$ \ mathbb p^1 $上的可构成变形，并通过诸如庞加莱等级1的不规则奇异性1 $，并概括了B. malgrange的先前结果。在本文的第二部分中，作为应用程序，我们证明了与单位和Euler Field一起的任何半神经形式的Frobenius歧管（超过$ \ Mathbb C $），都是Dubrovin-Frobenius歧管的分析性尖锐的细菌的完成。换句话说，任何形式的功率序列（提供WDVV方程的准源解，并在原点定义了半纤维frobenius代数）实际上是在没有进一步的驯服假设下收敛的。
In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincaré rank 1, and generalizing a previous result of B. Malgrange. In the second part of this paper, as an application, we prove that any semisimple formal Frobenius manifold (over $\mathbb C$), with unit and Euler field, is the completion of an analytic pointed germ of a Dubrovin-Frobenius manifold. In other words, any formal power series, which provides a quasi-homogenous solution of WDVV equations and defines a semisimple Frobenius algebra at the origin, is actually convergent under no further tameness assumptions.
