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The perturbation \\(f\\) is assumed to be locally Lipschitz near infinity and to satisfy a decay condition with rate \\(\\beta>0\\). The main new ingredient is a scale-dependent difference quotient argument, combined with a nonlocal potential method, which avoids differentiating \\(f\\) twice and yields quantitative Hessian convergence under only Lips","authors_text":"Jiguang Bao, Qinfeng Jiang","cross_cats":[],"headline":"Solutions to the supercritical Lagrangian mean curvature equation in two dimensions converge to quadratic polynomials at infinity under merely Lipschitz perturbations that decay at any positive rate.","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2026-04-29T03:04:02Z","title":"Optimal Asymptotic Behavior at Infinity for Solutions of the Supercritical Lagrangian Mean Curvature Equation in Exterior Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.26246","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T13:31:39.627365Z","id":"ef7c65a0-6f44-48d0-96cb-3728aef8af3e","model_set":{"reader":"grok-4.3"},"one_line_summary":"Solutions to the supercritical Lagrangian mean curvature equation in 2D exterior domains exhibit optimal asymptotic behavior at infinity under Lipschitz perturbations decaying at any positive rate.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Solutions to the supercritical Lagrangian mean curvature equation in two dimensions converge to quadratic polynomials at infinity under merely Lipschitz perturbations that decay at any positive rate.","strongest_claim":"This work generalizes the convergence results in [BJ2026], where f is required to be at least C^3 and β>2. 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