Year: 2026
Type: preprint
Abstract: We establish two nonuniqueness phenomena on $\mathbb{CP}^1$. First, distinct normalized positive-mass model potentials can have the same non-pluripolar Monge--Ampère measure. By the contact-set formula, their zero-contact sets agree $ω_{\mathrm{FS}}$-almost everywhere. Moreover, both have zero Lelong number at every point and identical multiplier ideal sheaves at every positive scale. Second, we construct distinct maximal test curves whose zero-contact sets agree pointwise at every parameter. Their inverse Legendre transforms are distinct bounded weak geodesic rays from zero with the same pointwise right initial tangent.
Source: arXiv (Cornell University)
Author: Xiao, Xia
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208776255
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