Curvature bounds on length-minimizing discs

Curvature bounds on length-minimizing discs | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Curvature bounds on length-minimizing discs Alexander Lytchak, Sophia Wagner This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3331246/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Mar, 2024 Read the published version in Geometriae Dedicata → Version 1 posted 7 You are reading this latest preprint version Abstract We show that a length-minimizing disk inherites the upper curvature bound of the target. As a consequence we prove that harmonic discs and ruled discs inherit the upper curvature bound from the ambient space. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Mar, 2024 Read the published version in Geometriae Dedicata → Version 1 posted Editorial decision: Revision requested 15 Dec, 2023 Reviews received at journal 11 Dec, 2023 Reviewers agreed at journal 13 Sep, 2023 Reviewers invited by journal 10 Sep, 2023 Editor assigned by journal 10 Sep, 2023 Submission checks completed at journal 06 Sep, 2023 First submitted to journal 06 Sep, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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