Matches in SemOpenAlex for { <https://semopenalex.org/work/W4225602358> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4225602358 abstract "In cite{CC1}, Cheeger-Colding considered manifolds with lower Ricci curvature bound and gave some almost rigidity results about warped products including almost metric cone rigidity and quantitative splitting theorem. As a generalization of manifolds with lower Ricci curvature bound, for metric measure spaces in $RCD(K, N)$, $1<N<infty$, splitting theorem cite{Gi13} and volume cone implies metric cone rigidity for balls and annuluses of a point cite{PG} have been proved. In this paper we will generalize Cheeger-Colding's cite{CC1} result about almost volume cone implies almost metric cone for annuluses of a compact subset to $RCD(K, N)$-spaces. More precisely, consider a $RCD(K, N)$-space $(X, d, mathfrak m)$ and a Borel subset $Omegasubset X$. If the closed subset $S=partial Omega$ has finite outer curvature, the diameter ${diam}(S)leq D$ and the mean curvature of $S$ satisfies $$m(x)leq m, , forall xin S,$$ and begin{equation*}mathfrak m(A_{a, b}(S))geq (1-epsilon)int_a^b left({sn}'_H(r)+ frac{m}{n-1}{sn}_H(r)right)^{n-1}dr mathfrak m_S(S)end{equation*} then $A_{a', b'}(S)$ is measured Gromov-Hausdorff close to a warped product $(a', b')times_{{sn}'_H(r)+ frac{m}{n-1}{sn}_H(r)}Y,$ $A_{a, b}(S)={xin Xsetminus Omega, , a<d(x, S)<b}$, $a<a'<b'<b$, $Y$ is a metric space with finite components with each component is a $RCD(0, N-1)$-space when $m=0, K=0$ and is a $RCD(N-2, N-1)$-space for other cases and $H=frac{K}{N-1}$. Note that when $m=0, K=0$, our result is a kind of quantitative splitting theorem and in other cases it is an almost metric cone rigidity. To prove this result, different from cite{Gi13, PG}, we will use cite{GiT}'s second order differentiation formula and a method similar as cite{CC1}." @default.
- W4225602358 created "2022-05-05" @default.
- W4225602358 creator A5003910460 @default.
- W4225602358 date "2021-12-17" @default.
- W4225602358 modified "2023-09-24" @default.
- W4225602358 title "Almost volume cone implies almost metric cone for annuluses centered at a compact set in $RCD(K, N)$-spaces" @default.
- W4225602358 doi "https://doi.org/10.48550/arxiv.2112.09353" @default.
- W4225602358 hasPublicationYear "2021" @default.
- W4225602358 type Work @default.
- W4225602358 citedByCount "0" @default.
- W4225602358 crossrefType "posted-content" @default.
- W4225602358 hasAuthorship W4225602358A5003910460 @default.
- W4225602358 hasBestOaLocation W42256023581 @default.
- W4225602358 hasConcept C11413529 @default.
- W4225602358 hasConcept C114614502 @default.
- W4225602358 hasConcept C12089564 @default.
- W4225602358 hasConcept C121332964 @default.
- W4225602358 hasConcept C134306372 @default.
- W4225602358 hasConcept C138187205 @default.
- W4225602358 hasConcept C149944404 @default.
- W4225602358 hasConcept C18648836 @default.
- W4225602358 hasConcept C195065555 @default.
- W4225602358 hasConcept C198043062 @default.
- W4225602358 hasConcept C2524010 @default.
- W4225602358 hasConcept C2779557605 @default.
- W4225602358 hasConcept C30014739 @default.
- W4225602358 hasConcept C33923547 @default.
- W4225602358 hasConcept C62520636 @default.
- W4225602358 hasConcept C77553402 @default.
- W4225602358 hasConceptScore W4225602358C11413529 @default.
- W4225602358 hasConceptScore W4225602358C114614502 @default.
- W4225602358 hasConceptScore W4225602358C12089564 @default.
- W4225602358 hasConceptScore W4225602358C121332964 @default.
- W4225602358 hasConceptScore W4225602358C134306372 @default.
- W4225602358 hasConceptScore W4225602358C138187205 @default.
- W4225602358 hasConceptScore W4225602358C149944404 @default.
- W4225602358 hasConceptScore W4225602358C18648836 @default.
- W4225602358 hasConceptScore W4225602358C195065555 @default.
- W4225602358 hasConceptScore W4225602358C198043062 @default.
- W4225602358 hasConceptScore W4225602358C2524010 @default.
- W4225602358 hasConceptScore W4225602358C2779557605 @default.
- W4225602358 hasConceptScore W4225602358C30014739 @default.
- W4225602358 hasConceptScore W4225602358C33923547 @default.
- W4225602358 hasConceptScore W4225602358C62520636 @default.
- W4225602358 hasConceptScore W4225602358C77553402 @default.
- W4225602358 hasLocation W42256023581 @default.
- W4225602358 hasOpenAccess W4225602358 @default.
- W4225602358 hasPrimaryLocation W42256023581 @default.
- W4225602358 hasRelatedWork W3021753 @default.
- W4225602358 hasRelatedWork W3100868007 @default.
- W4225602358 hasRelatedWork W36051980 @default.
- W4225602358 hasRelatedWork W38294843 @default.
- W4225602358 hasRelatedWork W40564664 @default.
- W4225602358 hasRelatedWork W42477737 @default.
- W4225602358 hasRelatedWork W46263998 @default.
- W4225602358 hasRelatedWork W52483380 @default.
- W4225602358 hasRelatedWork W57036774 @default.
- W4225602358 hasRelatedWork W60678892 @default.
- W4225602358 isParatext "false" @default.
- W4225602358 isRetracted "false" @default.
- W4225602358 workType "article" @default.