Matches in SemOpenAlex for { <https://semopenalex.org/work/W2949461916> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2949461916 abstract "We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the nearest cone. The monotonicity formulas are related to the classical Bishop-Gromov volume comparison theorem and Perelman's celebrated monotonicity formula for the Ricci flow. We will explain the connection between all of these. Moreover, we show that these new monotonicity formulas are linked to a new sharp gradient estimate for the Green's function that we prove. This is parallel to that Perelman's monotonicity is closely related to the sharp gradient estimate for the heat kernel of Li-Yau. In [CM4] we will use the monotonicity formulas we prove here to show uniqueness of certain tangent cones of Einstein manifolds and in [CM3] we will prove a number of related monotonicity formulas. Finally, there are obvious parallels between our monotonicity and the positive mass theorem of Schoen-Yau and Witten." @default.
- W2949461916 created "2019-06-27" @default.
- W2949461916 creator A5014724625 @default.
- W2949461916 date "2011-11-21" @default.
- W2949461916 modified "2023-09-27" @default.
- W2949461916 title "New monotonicity formulas for Ricci curvature and applications; I" @default.
- W2949461916 cites W1482228975 @default.
- W2949461916 cites W1498035120 @default.
- W2949461916 cites W1572732020 @default.
- W2949461916 cites W1870973791 @default.
- W2949461916 cites W1970157722 @default.
- W2949461916 cites W1970224775 @default.
- W2949461916 cites W1970564715 @default.
- W2949461916 cites W1975021249 @default.
- W2949461916 cites W1980017519 @default.
- W2949461916 cites W1987206679 @default.
- W2949461916 cites W2028338587 @default.
- W2949461916 cites W2028845750 @default.
- W2949461916 cites W2036708406 @default.
- W2949461916 cites W2040152921 @default.
- W2949461916 cites W2055064985 @default.
- W2949461916 cites W2061814576 @default.
- W2949461916 cites W2075354714 @default.
- W2949461916 cites W2075656243 @default.
- W2949461916 cites W2105973581 @default.
- W2949461916 cites W2107507588 @default.
- W2949461916 cites W2167912162 @default.
- W2949461916 cites W2323511938 @default.
- W2949461916 cites W3195885320 @default.
- W2949461916 hasPublicationYear "2011" @default.
- W2949461916 type Work @default.
- W2949461916 sameAs 2949461916 @default.
- W2949461916 citedByCount "0" @default.
- W2949461916 crossrefType "posted-content" @default.
- W2949461916 hasAuthorship W2949461916A5014724625 @default.
- W2949461916 hasConcept C12089564 @default.
- W2949461916 hasConcept C134306372 @default.
- W2949461916 hasConcept C138187205 @default.
- W2949461916 hasConcept C148729565 @default.
- W2949461916 hasConcept C149944404 @default.
- W2949461916 hasConcept C157157409 @default.
- W2949461916 hasConcept C195065555 @default.
- W2949461916 hasConcept C202444582 @default.
- W2949461916 hasConcept C2524010 @default.
- W2949461916 hasConcept C2777021972 @default.
- W2949461916 hasConcept C28903235 @default.
- W2949461916 hasConcept C33923547 @default.
- W2949461916 hasConcept C34388435 @default.
- W2949461916 hasConcept C72169020 @default.
- W2949461916 hasConceptScore W2949461916C12089564 @default.
- W2949461916 hasConceptScore W2949461916C134306372 @default.
- W2949461916 hasConceptScore W2949461916C138187205 @default.
- W2949461916 hasConceptScore W2949461916C148729565 @default.
- W2949461916 hasConceptScore W2949461916C149944404 @default.
- W2949461916 hasConceptScore W2949461916C157157409 @default.
- W2949461916 hasConceptScore W2949461916C195065555 @default.
- W2949461916 hasConceptScore W2949461916C202444582 @default.
- W2949461916 hasConceptScore W2949461916C2524010 @default.
- W2949461916 hasConceptScore W2949461916C2777021972 @default.
- W2949461916 hasConceptScore W2949461916C28903235 @default.
- W2949461916 hasConceptScore W2949461916C33923547 @default.
- W2949461916 hasConceptScore W2949461916C34388435 @default.
- W2949461916 hasConceptScore W2949461916C72169020 @default.
- W2949461916 hasLocation W29494619161 @default.
- W2949461916 hasOpenAccess W2949461916 @default.
- W2949461916 hasPrimaryLocation W29494619161 @default.
- W2949461916 hasRelatedWork W1576197206 @default.
- W2949461916 hasRelatedWork W1583875737 @default.
- W2949461916 hasRelatedWork W1598235945 @default.
- W2949461916 hasRelatedWork W1635895754 @default.
- W2949461916 hasRelatedWork W2000959256 @default.
- W2949461916 hasRelatedWork W2040152921 @default.
- W2949461916 hasRelatedWork W2101160220 @default.
- W2949461916 hasRelatedWork W2253464664 @default.
- W2949461916 hasRelatedWork W2900877016 @default.
- W2949461916 hasRelatedWork W2962813350 @default.
- W2949461916 hasRelatedWork W2963188479 @default.
- W2949461916 hasRelatedWork W2964161298 @default.
- W2949461916 hasRelatedWork W2964259716 @default.
- W2949461916 hasRelatedWork W2975897911 @default.
- W2949461916 hasRelatedWork W3008234884 @default.
- W2949461916 hasRelatedWork W3098916155 @default.
- W2949461916 hasRelatedWork W3100529882 @default.
- W2949461916 hasRelatedWork W3102358327 @default.
- W2949461916 hasRelatedWork W3165216388 @default.
- W2949461916 hasRelatedWork W60295252 @default.
- W2949461916 isParatext "false" @default.
- W2949461916 isRetracted "false" @default.
- W2949461916 magId "2949461916" @default.
- W2949461916 workType "article" @default.