{"paper":{"title":"Geometric obstructions to Lipschitz transport between weighted Hessian $\\mathrm{CD}(\\kappa,\\infty)$ manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.SP"],"primary_cat":"math.PR","authors_text":"Dan Mikulincer, William Dudarov","submitted_at":"2026-06-09T16:44:48Z","abstract_excerpt":"We construct a weighted Riemannian manifold $(\\mathbb R^2,g,\\mu)$ satisfying $\\mathrm{CD}(1/2,\\infty)$, the curvature-dimension condition, with the following property: if $\\gamma$ denotes a centered Gaussian measure on $\\mathbb R^2$, then every map $T:\\mathbb R^2 \\to \\mathbb R^2$ satisfying $T_\\#\\gamma=\\mu$ fails to be Lipschitz as a map from $(\\mathbb R^2,\\|\\cdot\\|)$ to $(\\mathbb R^2,g)$.\n  Building on this, we prove a Weyl asymptotic law for the eigenvalues of the weighted Laplacian $-\\Delta_{g,\\mu}$ and show that they are asymptotically negligible when compared to the eigenvalues of $-\\Delt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11085","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11085/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"}