{"paper":{"title":"On Mahler's conjecture for even s-concave functions in dimensions 1 and 2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Elie Nakhle, Matthieu Fradelizi","submitted_at":"2024-12-16T22:05:55Z","abstract_excerpt":"In this paper, we establish different sharp forms of Mahler's conjecture for $s$-concave even functions in dimensions $n$, for $n=1$ and $2$, for $s>-1/n$, thus generalizing our previous results in \\cite{FN} on log-concave even functions in dimension 2, which corresponds to the case $s=0$. The functional volume product of an even $s$-concave function $g$ is \\[ \\int_{\\mathbb{R}^{n}}g(x)dx\\int_{\\mathbb{R}^{n}}\\mathcal{L}_{s}g(y)dy, \\] where $\\mathcal{L}_{s}g$ is the $s$-polar function associated to $g$. The analogue of Mahler's conjecture for even $s$-concave functions postulates that this quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12372","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.12372/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}