Matches in SemOpenAlex for { <https://semopenalex.org/work/W4366999530> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4366999530 abstract "We prove several analogs of Gromov's macroscopic dimension conjecture with extra curvature assumptions. More explicitly, we show that for an open Riemannian $n$-manifold $(M,g)$ of nonnegative Ricci (resp. sectional) curvature, if it has uniformly positive scalar curvature and it is uniformly volume noncollapsed, then the essential (resp. Hausdorff) dimension of an asymptotic cone, as a notion of largeness, has a sharp upper bound $n-2$, which is $2$ less than the upper bound for an open Riemannian manifold with only nonnegative Ricci curvature. As a consequence, the dimension of space of linear growth harmonic functions of $M$ has upper bound $n-1$ which is also $2$ less than the sharp bound $n+1$ when $M$ only has nonnegative Ricci curvature. We also prove the first Betti number upper bound is $n-2$ if $M$ is compact and a fibration theorem over torus, then a rigidity theorem for the fiber." @default.
- W4366999530 created "2023-04-27" @default.
- W4366999530 creator A5057603213 @default.
- W4366999530 date "2023-04-22" @default.
- W4366999530 modified "2023-10-18" @default.
- W4366999530 title "Two-dimension vanishing, splitting and positive scalar curvature" @default.
- W4366999530 doi "https://doi.org/10.48550/arxiv.2304.11466" @default.
- W4366999530 hasPublicationYear "2023" @default.
- W4366999530 type Work @default.
- W4366999530 citedByCount "0" @default.
- W4366999530 crossrefType "posted-content" @default.
- W4366999530 hasAuthorship W4366999530A5057603213 @default.
- W4366999530 hasBestOaLocation W43669995301 @default.
- W4366999530 hasConcept C114614502 @default.
- W4366999530 hasConcept C12089564 @default.
- W4366999530 hasConcept C12520029 @default.
- W4366999530 hasConcept C129621563 @default.
- W4366999530 hasConcept C134306372 @default.
- W4366999530 hasConcept C14196021 @default.
- W4366999530 hasConcept C194198291 @default.
- W4366999530 hasConcept C195065555 @default.
- W4366999530 hasConcept C202444582 @default.
- W4366999530 hasConcept C2524010 @default.
- W4366999530 hasConcept C2780990831 @default.
- W4366999530 hasConcept C33923547 @default.
- W4366999530 hasConcept C42448751 @default.
- W4366999530 hasConcept C54486226 @default.
- W4366999530 hasConcept C5961521 @default.
- W4366999530 hasConcept C77553402 @default.
- W4366999530 hasConceptScore W4366999530C114614502 @default.
- W4366999530 hasConceptScore W4366999530C12089564 @default.
- W4366999530 hasConceptScore W4366999530C12520029 @default.
- W4366999530 hasConceptScore W4366999530C129621563 @default.
- W4366999530 hasConceptScore W4366999530C134306372 @default.
- W4366999530 hasConceptScore W4366999530C14196021 @default.
- W4366999530 hasConceptScore W4366999530C194198291 @default.
- W4366999530 hasConceptScore W4366999530C195065555 @default.
- W4366999530 hasConceptScore W4366999530C202444582 @default.
- W4366999530 hasConceptScore W4366999530C2524010 @default.
- W4366999530 hasConceptScore W4366999530C2780990831 @default.
- W4366999530 hasConceptScore W4366999530C33923547 @default.
- W4366999530 hasConceptScore W4366999530C42448751 @default.
- W4366999530 hasConceptScore W4366999530C54486226 @default.
- W4366999530 hasConceptScore W4366999530C5961521 @default.
- W4366999530 hasConceptScore W4366999530C77553402 @default.
- W4366999530 hasLocation W43669995301 @default.
- W4366999530 hasOpenAccess W4366999530 @default.
- W4366999530 hasPrimaryLocation W43669995301 @default.
- W4366999530 hasRelatedWork W2005988006 @default.
- W4366999530 hasRelatedWork W2297585950 @default.
- W4366999530 hasRelatedWork W2369913733 @default.
- W4366999530 hasRelatedWork W2377944149 @default.
- W4366999530 hasRelatedWork W4223616807 @default.
- W4366999530 hasRelatedWork W4226246021 @default.
- W4366999530 hasRelatedWork W4293156355 @default.
- W4366999530 hasRelatedWork W4319781469 @default.
- W4366999530 hasRelatedWork W4366999530 @default.
- W4366999530 hasRelatedWork W2948366196 @default.
- W4366999530 isParatext "false" @default.
- W4366999530 isRetracted "false" @default.
- W4366999530 workType "article" @default.