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Some polynomial spaces are Euclidean balls
Abstract
In this paper, we establish a matrix criterion for a space to be homeomorphic to a closed Euclidean ball. As applications, we prove that the normalized space of K-Lorentzian polynomials on an arbitrary open convex cone K is homeomorphic to a closed Euclidean ball, giving an affirmative answer to Brändén and Leake's question, and we also settle Brändén's conjecture that the normalized space of homogeneous multiaffine real stable polynomials is homeomorphic to a closed Euclidean ball. In addition, our results show that the normalized space of homogeneous K-stable polynomials of degree d is homeomorphic to a closed Euclidean ball.
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BibTeX
@misc{dong2026some,
title = {{Some polynomial spaces are Euclidean balls}},
author = {Yuxian Dong and Wenle Shi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08265},
eprint = {2611.08265},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08265},
}
RIS
TY - UNPB
TI - Some polynomial spaces are Euclidean balls
AU - Yuxian Dong
AU - Wenle Shi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08265
UR - https://arxiv.org/abs/2611.08265
AB - In this paper, we establish a matrix criterion for a space to be homeomorphic to a closed Euclidean ball. As applications, we prove that the normalized space of K-Lorentzian polynomials on an arbitrary open convex cone K is homeomorphic to a closed Euclidean ball, giving an affirmative answer to Brändén and Leake's question, and we also settle Brändén's conjecture that the normalized space of homogeneous multiaffine real stable polynomials is homeomorphic to a closed Euclidean ball. In addition, our results show that the normalized space of homogeneous K-stable polynomials of degree d is homeomorphic to a closed Euclidean ball.
ER -