Author

Yi-Peng Zhang

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Preprint Sep 2026

$\varepsilon$-isometries without isometric embeddings

We show that there exist two separable real Banach spaces $X$ and $Y$ such that, for every $\varepsilon>0$, there is a standard exact $\varepsilon$-isometry $f_\varepsilon: X\to Y$ whose distortion of every distance is between $0$ and $\varepsilon$, whereas no isometric embedding of $X$ into $Y$ exists, even without a...

Long-Fa Sun, Yi-Peng Zhang · 0 citations

Preprint Sep 2026

The Optimal Scaling Parameter in Metric Cotype for Alexandrov Spaces of Nonnegative Curvature

We determine the optimal order of the scaling parameter in the metric cotype $2$ inequality for complete Alexandrov spaces of nonnegative curvature. It grows linearly with the dimension $n$ of the discrete torus. This answers Question 17 of Eskenazis, Mendel, and Naor. In their sign-vector normalization on $\bigl(\math...

Qing-Jin Cheng, Long-Fa Sun, Yi-Peng Zhang · 0 citations