{"paper":{"title":"Stable Gaussian Minimal Bubbles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.PR","authors_text":"Steven Heilman","submitted_at":"2019-01-13T04:34:42Z","abstract_excerpt":"It is shown that $3$ disjoint sets with fixed Gaussian volumes that partition $\\mathbb{R}^{n}$ with nearly minimum total Gaussian surface area must be close to adjacent $120$ degree sectors, when $n\\geq2$. These same results hold for any number $m\\leq n+1$ of sets partitioning $\\mathbb{R}^{n}$, conditional on the solution of a finite-dimensional optimization problem (similar to the endpoint case of the Plurality is Stablest Problem, or the Propeller Conjecture of Khot and Naor). When $m>3$, the minimal Gaussian surface area is achieved by the cones over a regular simplex. We therefore strength"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03934","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}