Matches in SemOpenAlex for { <https://semopenalex.org/work/W4299125103> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4299125103 abstract "We define a formal Riemannian metric on a given conformal class of metrics on a closed Riemann surface. We show interesting formal properties for this metric, in particular the curvature is nonpositive and the Liouville energy is geodesically convex. The geodesic equation for this metric corresponds to a degenerate elliptic fully nonlinear PDE, and we prove that any two points are connected by a $C^{1,1}$ geodesic. Using this we can define a length space structure on the given conformal class. We present a different approach to the uniformization theorem by studying the negative gradient flow of the normalized Liouville energy, a new geometric flow whose principal term is the inverse of the Gauss curvature. We prove long time existence of solutions with arbitrary initial data and weak convergence to constant scalar curvature metrics. This is all a special case of a more general construction on even dimensional manifolds related to the $sigma_{frac{n}{2}}$-Yamabe problem, which will appear in a forthcoming article." @default.
- W4299125103 created "2022-10-02" @default.
- W4299125103 creator A5000069215 @default.
- W4299125103 creator A5028362435 @default.
- W4299125103 date "2015-07-16" @default.
- W4299125103 modified "2023-09-26" @default.
- W4299125103 title "A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow" @default.
- W4299125103 doi "https://doi.org/10.48550/arxiv.1507.04781" @default.
- W4299125103 hasPublicationYear "2015" @default.
- W4299125103 type Work @default.
- W4299125103 citedByCount "0" @default.
- W4299125103 crossrefType "posted-content" @default.
- W4299125103 hasAuthorship W4299125103A5000069215 @default.
- W4299125103 hasAuthorship W4299125103A5028362435 @default.
- W4299125103 hasBestOaLocation W42991251031 @default.
- W4299125103 hasConcept C105795698 @default.
- W4299125103 hasConcept C113758315 @default.
- W4299125103 hasConcept C12520029 @default.
- W4299125103 hasConcept C134306372 @default.
- W4299125103 hasConcept C149260544 @default.
- W4299125103 hasConcept C158917313 @default.
- W4299125103 hasConcept C16140857 @default.
- W4299125103 hasConcept C163836022 @default.
- W4299125103 hasConcept C165818556 @default.
- W4299125103 hasConcept C195065555 @default.
- W4299125103 hasConcept C202444582 @default.
- W4299125103 hasConcept C207467116 @default.
- W4299125103 hasConcept C2524010 @default.
- W4299125103 hasConcept C2779668893 @default.
- W4299125103 hasConcept C33923547 @default.
- W4299125103 hasConcept C42448751 @default.
- W4299125103 hasConcept C98214594 @default.
- W4299125103 hasConcept C98763669 @default.
- W4299125103 hasConceptScore W4299125103C105795698 @default.
- W4299125103 hasConceptScore W4299125103C113758315 @default.
- W4299125103 hasConceptScore W4299125103C12520029 @default.
- W4299125103 hasConceptScore W4299125103C134306372 @default.
- W4299125103 hasConceptScore W4299125103C149260544 @default.
- W4299125103 hasConceptScore W4299125103C158917313 @default.
- W4299125103 hasConceptScore W4299125103C16140857 @default.
- W4299125103 hasConceptScore W4299125103C163836022 @default.
- W4299125103 hasConceptScore W4299125103C165818556 @default.
- W4299125103 hasConceptScore W4299125103C195065555 @default.
- W4299125103 hasConceptScore W4299125103C202444582 @default.
- W4299125103 hasConceptScore W4299125103C207467116 @default.
- W4299125103 hasConceptScore W4299125103C2524010 @default.
- W4299125103 hasConceptScore W4299125103C2779668893 @default.
- W4299125103 hasConceptScore W4299125103C33923547 @default.
- W4299125103 hasConceptScore W4299125103C42448751 @default.
- W4299125103 hasConceptScore W4299125103C98214594 @default.
- W4299125103 hasConceptScore W4299125103C98763669 @default.
- W4299125103 hasLocation W42991251031 @default.
- W4299125103 hasOpenAccess W4299125103 @default.
- W4299125103 hasPrimaryLocation W42991251031 @default.
- W4299125103 hasRelatedWork W2016551758 @default.
- W4299125103 hasRelatedWork W2046001483 @default.
- W4299125103 hasRelatedWork W2070837384 @default.
- W4299125103 hasRelatedWork W2086781502 @default.
- W4299125103 hasRelatedWork W2249456521 @default.
- W4299125103 hasRelatedWork W2328219387 @default.
- W4299125103 hasRelatedWork W2923401817 @default.
- W4299125103 hasRelatedWork W4244326923 @default.
- W4299125103 hasRelatedWork W4379089548 @default.
- W4299125103 hasRelatedWork W4380136192 @default.
- W4299125103 isParatext "false" @default.
- W4299125103 isRetracted "false" @default.
- W4299125103 workType "article" @default.