Author

Eric Shen

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Preprint Sep 2026

Rayleigh-Residual Flow I: Normal Matrices

We study the squared Rayleigh-residual functional on complex projective space and its negative gradient flow. For an arbitrary complex matrix, every positive-residual critical point has a strictly descending tangent direction; consequently, the local minima are precisely the eigenlines. For normal matrices, we describe...

Eric Shen · 0 citations

Preprint Aug 2026

The Zaporozhets-Tarasov Conjecture on Mean Distances

For a convex body $K \subset \mathbb R^d$ let $\Delta(K)$ be the expected distance between two independent uniform points of $K$, and let $\theta(K)$ be the corresponding expectation for normalized surface measure on $\partial K$. The Zaporozhets-Tarasov conjecture asserts $\Delta(K) \le \theta(K)$. We prove this conje...

Eric Shen · 0 citations