We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz, and that the eigenvalues of its Jacobian have controlled growth at infinity.

中文翻译：

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对数凹测度上的最优传输图的界限

我们考虑严格的对数凹测度，其边界在无穷远处退化。我们证明了从高斯到这种度量的最佳传输映射是局部 Lipschitz，并且其雅可比矩阵的特征值控制了无穷远的增长。