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As a corollary, we can find many constant scalar curvature K\\\"ahler metrics with $c_1<0$. Using the same method, we also prove a similar result for the deformed Hermitian-Yang-Mills equation when the angle is in $(\\frac{n\\pi}{2}-\\frac{\\pi}{4},\\frac{n\\pi}{2})$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.10222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-24T13:20:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c94ce588b4bf718767a5b870e66bc698b34ef3e9cb0b4aaa0c8e08897c27bd04","abstract_canon_sha256":"874355849a22bac9665c1d99525f0955632624e77976374d789e835e414916ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:59:01.051781Z","signature_b64":"k9dhuthCN/ZY/SJ1nXWoeBn7KfxClhz5ZgbrG+jmJ0Sb9klbrg+CcdRdq3Jp+WSC8/4zuH+0c0yh4rNkJgjuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb48780ff5e5f1cb0ba3dde214029ec3d98e1b5d01f002646fda69e460ea6618","last_reissued_at":"2026-07-05T02:59:01.051350Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:59:01.051350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On J-equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Gao Chen","submitted_at":"2019-05-24T13:20:39Z","abstract_excerpt":"In this paper, we prove that for any K\\\"ahler metrics $\\omega_0$ and $\\chi$ on $M$, there exists $\\omega_\\varphi=\\omega_0+\\sqrt{-1}\\partial\\bar\\partial\\varphi>0$ satisfying the J-equation $\\mathrm{tr}_{\\omega_\\varphi}\\chi=c$ if and only if $(M,[\\omega_0],[\\chi])$ is uniformly J-stable. As a corollary, we can find many constant scalar curvature K\\\"ahler metrics with $c_1<0$. 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