Matches in SemOpenAlex for { <https://semopenalex.org/work/W4297580903> ?p ?o ?g. }
Showing items 1 to 54 of
54
with 100 items per page.
- W4297580903 abstract "Let $D$ be a Riemannian 2-disc of area $A$, diameter $d$ and length of the boundary $L$. We prove that it is possible to contract the boundary of $D$ through curves of length $leq L + 200dmax{1,ln {sqrt{A}over d} }$. This answers a twenty-year old question of S. Frankel and M. Katz, a version of which was asked earlier by M.Gromov. We also prove that a Riemannian $2$-sphere $M$ of diameter $d$ and area $A$ can be swept out by loops based at any prescribed point $pin M$ of length $leq 200 dmax{1,ln{sqrt{A}over d} }$. This estimate is optimal up to a constant factor. In addition, we provide much better (and nearly optimal) estimates for these problems in the case, when $A<<d^2$. Finally, we describe the applications of our estimates for study of lengths of various geodesics between a fixed pair of points on thin Riemannian $2$-spheres." @default.
- W4297580903 created "2022-09-30" @default.
- W4297580903 creator A5033217028 @default.
- W4297580903 creator A5035125984 @default.
- W4297580903 creator A5043918843 @default.
- W4297580903 date "2012-05-24" @default.
- W4297580903 modified "2023-10-14" @default.
- W4297580903 title "Contracting the boundary of a Riemannian 2-disc" @default.
- W4297580903 doi "https://doi.org/10.48550/arxiv.1205.5474" @default.
- W4297580903 hasPublicationYear "2012" @default.
- W4297580903 type Work @default.
- W4297580903 citedByCount "0" @default.
- W4297580903 crossrefType "posted-content" @default.
- W4297580903 hasAuthorship W4297580903A5033217028 @default.
- W4297580903 hasAuthorship W4297580903A5035125984 @default.
- W4297580903 hasAuthorship W4297580903A5043918843 @default.
- W4297580903 hasBestOaLocation W42975809031 @default.
- W4297580903 hasConcept C114614502 @default.
- W4297580903 hasConcept C121332964 @default.
- W4297580903 hasConcept C1276947 @default.
- W4297580903 hasConcept C134306372 @default.
- W4297580903 hasConcept C165818556 @default.
- W4297580903 hasConcept C2524010 @default.
- W4297580903 hasConcept C28719098 @default.
- W4297580903 hasConcept C33923547 @default.
- W4297580903 hasConcept C62354387 @default.
- W4297580903 hasConcept C72422203 @default.
- W4297580903 hasConceptScore W4297580903C114614502 @default.
- W4297580903 hasConceptScore W4297580903C121332964 @default.
- W4297580903 hasConceptScore W4297580903C1276947 @default.
- W4297580903 hasConceptScore W4297580903C134306372 @default.
- W4297580903 hasConceptScore W4297580903C165818556 @default.
- W4297580903 hasConceptScore W4297580903C2524010 @default.
- W4297580903 hasConceptScore W4297580903C28719098 @default.
- W4297580903 hasConceptScore W4297580903C33923547 @default.
- W4297580903 hasConceptScore W4297580903C62354387 @default.
- W4297580903 hasConceptScore W4297580903C72422203 @default.
- W4297580903 hasLocation W42975809031 @default.
- W4297580903 hasLocation W42975809032 @default.
- W4297580903 hasOpenAccess W4297580903 @default.
- W4297580903 hasPrimaryLocation W42975809031 @default.
- W4297580903 hasRelatedWork W135690750 @default.
- W4297580903 hasRelatedWork W1611923313 @default.
- W4297580903 hasRelatedWork W2023206826 @default.
- W4297580903 hasRelatedWork W2382024233 @default.
- W4297580903 hasRelatedWork W2906488785 @default.
- W4297580903 hasRelatedWork W2950655538 @default.
- W4297580903 hasRelatedWork W4214786028 @default.
- W4297580903 hasRelatedWork W4287904723 @default.
- W4297580903 hasRelatedWork W4289388887 @default.
- W4297580903 hasRelatedWork W4214960857 @default.
- W4297580903 isParatext "false" @default.
- W4297580903 isRetracted "false" @default.
- W4297580903 workType "article" @default.