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Triangles minimize the Monge-Ampère eigenvalue among planar bounded convex domains of a given area
Abstract
We prove that triangles minimize the Monge-Ampère eigenvalue among bounded planar convex domains of a given area, thus resolving the two-dimensional case of Le's simplex conjecture for the Monge-Ampère eigenvalue (The eigenvalue problem for the Monge-Ampère operator on general bounded convex domains, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018)). The proof uses a neighbor-decreasing property of the Monge-Ampère eigenvalues of convex polygons along vertex elimination parallel chord movements.
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BibTeX
@misc{gu2026triangles,
title = {{Triangles minimize the Monge-Ampère eigenvalue among planar bounded convex domains of a given area}},
author = {Chong Gu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15563},
eprint = {2609.15563},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15563},
}
RIS
TY - UNPB
TI - Triangles minimize the Monge-Ampère eigenvalue among planar bounded convex domains of a given area
AU - Chong Gu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.15563
UR - https://arxiv.org/abs/2609.15563
AB - We prove that triangles minimize the Monge-Ampère eigenvalue among bounded planar convex domains of a given area, thus resolving the two-dimensional case of Le's simplex conjecture for the Monge-Ampère eigenvalue (The eigenvalue problem for the Monge-Ampère operator on general bounded convex domains, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018)). The proof uses a neighbor-decreasing property of the Monge-Ampère eigenvalues of convex polygons along vertex elimination parallel chord movements.
ER -