https://neckpinch.com/authors/ryosuke-nomura/New arXiv papers by Ryosuke Nomura, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1802.05425/arxiv:1802.05425Thu, 15 Feb 2018 00:00:00 GMTRyosuke Nomura — In this paper, we prove the Miyaoka-Yau inequality for compact Kähler manifolds with semi-positive canonical bundle. The key point of the proof is the estimate for the L²-norm of the scalar curvature along the Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometryScalar curvature https://neckpinch.com/papers/1610.01976/arxiv:1610.01976Thu, 06 Oct 2016 00:00:00 GMTRyosuke Nomura — Recently, Wu-Yau and Tosatti-Yang established the connection between the negativity of holomorphic sectional curvatures and the positivity of canonical bundles for compact Kähler manifolds. In this short note, we give anothe proof of their theorems by using the Kähler-Ricci flow.Ricci flowKähler–Ricci flowKähler geometry https://neckpinch.com/papers/1607.03004/arxiv:1607.03004Mon, 11 Jul 2016 00:00:00 GMTRyosuke Nomura — We investigate the scalar curvature behavior along the normalized conical Kähler-Ricci flow ωₜ, which is the conic version of the normalized Kähler-Ricci flow, with finite maximal existence time T<∞. We prove that the scalar curvature of ωₜ is bounded from above by C/(T-t)² under the existence of a contraction associated to the limiting cohomology class [ω_T]. This generalizes Z. Zhang's work to the conic case.Ricci flowKähler–Ricci flowSingularitiesKähler geometryScalar curvature