FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308199600> ?p ?o ?g. }

• W4308199600 endingPage "1905" @default.
• W4308199600 startingPage "1849" @default.
• W4308199600 abstract "Democritus and the early atomists held that the material cause of all things that exist is the coming together of atoms and void. Atoms are eternal and have many different shapes, and they can cluster together to create things that are perceivable. Differences in shape, arrangement, and position of atoms produce different phenomena. Like the atoms of Democritus, the Grim Reaper solution to curve shortening flow is eternal and indivisible -- it does not split off a line, and is itself its only asymptotic translator. Confirming the heuristic described by Huisken and Sinestrari [J. Differential Geom. 101, 2 (2015), 267-287], we show that it gives rise to a great diversity of convex ancient and translating solutions to mean curvature flow, through the evolution of families of Grim hyperplanes in suitable configurations. We construct, in all dimensions $nge 2$, a large family of new examples, including both symmetric and asymmetric examples, as well as many eternal examples that do not evolve by translation. The latter resolve a conjecture of White [J. Amer. Math. Soc. 16, 1 (2003), 123-138]. We also provide a detailed asymptotic analysis of convex ancient solutions in slab regions in general. Roughly speaking, we show that they decompose backwards in time into a canonical configuration of Grim hyperplanes which satisfies certain necessary conditions. An analogous decomposition holds forwards in time for eternal solutions. One consequence is a new rigidity result for translators. Another is that, in dimension two, solutions are necessarily reflection symmetric across the mid-plane of their slab." @default.
• W4308199600 created "2022-11-09" @default.
• W4308199600 creator A5000849080 @default.
• W4308199600 creator A5062440305 @default.
• W4308199600 creator A5065181230 @default.
• W4308199600 date "2022-10-28" @default.
• W4308199600 modified "2023-09-23" @default.
• W4308199600 title "Ancient mean curvature flows out of polytopes" @default.
• W4308199600 cites W1491650242 @default.
• W4308199600 cites W1509420504 @default.
• W4308199600 cites W1515873116 @default.
• W4308199600 cites W1530161281 @default.
• W4308199600 cites W1538338229 @default.
• W4308199600 cites W1569084793 @default.
• W4308199600 cites W1586829048 @default.
• W4308199600 cites W1606513471 @default.
• W4308199600 cites W1922667232 @default.
• W4308199600 cites W1967984121 @default.
• W4308199600 cites W1980264098 @default.
• W4308199600 cites W1980936095 @default.
• W4308199600 cites W1983621961 @default.
• W4308199600 cites W1993384004 @default.
• W4308199600 cites W1994691196 @default.
• W4308199600 cites W2021350139 @default.
• W4308199600 cites W2049356963 @default.
• W4308199600 cites W2057061707 @default.
• W4308199600 cites W2068072598 @default.
• W4308199600 cites W2069140940 @default.
• W4308199600 cites W2083796387 @default.
• W4308199600 cites W2095345234 @default.
• W4308199600 cites W2112767657 @default.
• W4308199600 cites W2119790810 @default.
• W4308199600 cites W2132783695 @default.
• W4308199600 cites W2172197630 @default.
• W4308199600 cites W2622334219 @default.
• W4308199600 cites W2727793566 @default.
• W4308199600 cites W2735664388 @default.
• W4308199600 cites W2761812841 @default.
• W4308199600 cites W2791349169 @default.
• W4308199600 cites W2920651408 @default.
• W4308199600 cites W2962827916 @default.
• W4308199600 cites W2962876353 @default.
• W4308199600 cites W2963067241 @default.
• W4308199600 cites W2963085897 @default.
• W4308199600 cites W2963321253 @default.
• W4308199600 cites W2963676500 @default.
• W4308199600 cites W2963713040 @default.
• W4308199600 cites W2979745158 @default.
• W4308199600 cites W3011377240 @default.
• W4308199600 cites W3016091200 @default.
• W4308199600 cites W3024255744 @default.
• W4308199600 cites W3033601432 @default.
• W4308199600 cites W3035602188 @default.
• W4308199600 cites W3043159255 @default.
• W4308199600 cites W3080769870 @default.
• W4308199600 cites W3083888084 @default.
• W4308199600 cites W3093299691 @default.
• W4308199600 cites W3098292724 @default.
• W4308199600 cites W3100604322 @default.
• W4308199600 cites W3113288029 @default.
• W4308199600 cites W3123120920 @default.
• W4308199600 cites W3125513853 @default.
• W4308199600 cites W3196168312 @default.
• W4308199600 cites W3199763657 @default.
• W4308199600 cites W3203122501 @default.
• W4308199600 cites W4210631977 @default.
• W4308199600 cites W4229538311 @default.
• W4308199600 doi "https://doi.org/10.2140/gt.2022.26.1849" @default.
• W4308199600 hasPublicationYear "2022" @default.
• W4308199600 type Work @default.
• W4308199600 citedByCount "1" @default.
• W4308199600 countsByYear W43081996002023 @default.
• W4308199600 crossrefType "journal-article" @default.
• W4308199600 hasAuthorship W4308199600A5000849080 @default.
• W4308199600 hasAuthorship W4308199600A5062440305 @default.
• W4308199600 hasAuthorship W4308199600A5065181230 @default.
• W4308199600 hasBestOaLocation W43081996002 @default.
• W4308199600 hasConcept C112680207 @default.
• W4308199600 hasConcept C114614502 @default.
• W4308199600 hasConcept C127813850 @default.
• W4308199600 hasConcept C143669375 @default.
• W4308199600 hasConcept C175017881 @default.
• W4308199600 hasConcept C195065555 @default.
• W4308199600 hasConcept C202444582 @default.
• W4308199600 hasConcept C2524010 @default.
• W4308199600 hasConcept C2780990831 @default.
• W4308199600 hasConcept C33923547 @default.
• W4308199600 hasConcept C68693459 @default.
• W4308199600 hasConceptScore W4308199600C112680207 @default.
• W4308199600 hasConceptScore W4308199600C114614502 @default.
• W4308199600 hasConceptScore W4308199600C127813850 @default.
• W4308199600 hasConceptScore W4308199600C143669375 @default.
• W4308199600 hasConceptScore W4308199600C175017881 @default.
• W4308199600 hasConceptScore W4308199600C195065555 @default.
• W4308199600 hasConceptScore W4308199600C202444582 @default.
• W4308199600 hasConceptScore W4308199600C2524010 @default.
• W4308199600 hasConceptScore W4308199600C2780990831 @default.
• W4308199600 hasConceptScore W4308199600C33923547 @default.

• next