{"paper":{"title":"Existence Results for the Nonlinear Hodge Minimal Surface Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Agress","submitted_at":"2018-03-06T00:50:53Z","abstract_excerpt":"Given a compact Riemannian manifold $(M^n,g)$ and a fixed cohomology class, $[\\alpha^*] \\in H^k(M)$, we consider the existence of a minimizer $\\alpha \\in [\\alpha^*]$ of the generalized minimal surface energy $\\int_M \\sqrt{1+|\\alpha|^2} dV_g$. When $k = 1$, we prove the existence of unique minimizers for every cohomology class $[\\alpha^*]$. Next, when $k > 1$, we construct examples of singular solutions for finite cohomology class $[\\alpha^*] \\in H^k(S^k \\times S^k,g)$, where $g$ is conformal to the standard metric on $S^k \\times S^k$. Additionally, we show that when $k=2$, these singular solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01970","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":""},"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"}