Matches in SemOpenAlex for { <https://semopenalex.org/work/W3215726571> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W3215726571 abstract "Surfaces that evolve by mean curvature flow develop singularities. These singularities can be modeled by self-shrinkers, surfaces that shrink by dilations under the flow. Singularities modeled on classical self-shrinkers, namely spheres and cylinders, are stable under perturbations of the flow. In contrast, singularities modeled on other self-shrinkers, such as the Angenent torus, are unstable: perturbing the flow will generally change the kind of singularity. One can measure the degree of instability by computing the Morse index of the self-shrinker, viewed as a critical point of an appropriate functional. In this paper, we present a numerical method for computing the index of rotationally symmetric self-shrinkers. We apply this method to the Angenent torus, the first known nontrivial example of a self-shrinker. We obtain strong numerical evidence that, excluding dilations and translations, the index of the Angenent torus is 5, which is consistent with the lower bound of 3 from the work of Liu and the upper bound of 29 from our earlier work. Also, we unexpectedly discover two additional variations of the Angenent torus with eigenvalue $$-1$$ ." @default.
- W3215726571 created "2021-12-06" @default.
- W3215726571 creator A5089033864 @default.
- W3215726571 date "2021-11-26" @default.
- W3215726571 modified "2023-09-26" @default.
- W3215726571 title "Numerically Computing the Index of Mean Curvature Flow Self-Shrinkers" @default.
- W3215726571 cites W1980017519 @default.
- W3215726571 cites W1998965679 @default.
- W3215726571 cites W2032214088 @default.
- W3215726571 cites W2035194117 @default.
- W3215726571 cites W2963422092 @default.
- W3215726571 cites W2963425269 @default.
- W3215726571 cites W2963799523 @default.
- W3215726571 cites W2964177183 @default.
- W3215726571 cites W2976551932 @default.
- W3215726571 cites W2981444786 @default.
- W3215726571 cites W2986549395 @default.
- W3215726571 cites W3045441864 @default.
- W3215726571 cites W3087641683 @default.
- W3215726571 cites W3098183438 @default.
- W3215726571 cites W3098344011 @default.
- W3215726571 cites W3105289155 @default.
- W3215726571 cites W4229538311 @default.
- W3215726571 doi "https://doi.org/10.1007/s00025-021-01550-y" @default.
- W3215726571 hasPublicationYear "2021" @default.
- W3215726571 type Work @default.
- W3215726571 sameAs 3215726571 @default.
- W3215726571 citedByCount "1" @default.
- W3215726571 countsByYear W32157265712021 @default.
- W3215726571 crossrefType "journal-article" @default.
- W3215726571 hasAuthorship W3215726571A5089033864 @default.
- W3215726571 hasBestOaLocation W32157265712 @default.
- W3215726571 hasConcept C127813850 @default.
- W3215726571 hasConcept C12843 @default.
- W3215726571 hasConcept C134306372 @default.
- W3215726571 hasConcept C16171025 @default.
- W3215726571 hasConcept C175017881 @default.
- W3215726571 hasConcept C195065555 @default.
- W3215726571 hasConcept C2524010 @default.
- W3215726571 hasConcept C33923547 @default.
- W3215726571 hasConcept C38349280 @default.
- W3215726571 hasConcept C77553402 @default.
- W3215726571 hasConcept C9767117 @default.
- W3215726571 hasConceptScore W3215726571C127813850 @default.
- W3215726571 hasConceptScore W3215726571C12843 @default.
- W3215726571 hasConceptScore W3215726571C134306372 @default.
- W3215726571 hasConceptScore W3215726571C16171025 @default.
- W3215726571 hasConceptScore W3215726571C175017881 @default.
- W3215726571 hasConceptScore W3215726571C195065555 @default.
- W3215726571 hasConceptScore W3215726571C2524010 @default.
- W3215726571 hasConceptScore W3215726571C33923547 @default.
- W3215726571 hasConceptScore W3215726571C38349280 @default.
- W3215726571 hasConceptScore W3215726571C77553402 @default.
- W3215726571 hasConceptScore W3215726571C9767117 @default.
- W3215726571 hasIssue "1" @default.
- W3215726571 hasLocation W32157265711 @default.
- W3215726571 hasLocation W32157265712 @default.
- W3215726571 hasOpenAccess W3215726571 @default.
- W3215726571 hasPrimaryLocation W32157265711 @default.
- W3215726571 hasRelatedWork W1521624701 @default.
- W3215726571 hasRelatedWork W1581293618 @default.
- W3215726571 hasRelatedWork W2147547225 @default.
- W3215726571 hasRelatedWork W2951043176 @default.
- W3215726571 hasRelatedWork W2953308620 @default.
- W3215726571 hasRelatedWork W2963815675 @default.
- W3215726571 hasRelatedWork W4283838230 @default.
- W3215726571 hasRelatedWork W4301385768 @default.
- W3215726571 hasRelatedWork W4301906044 @default.
- W3215726571 hasRelatedWork W4302011306 @default.
- W3215726571 hasVolume "77" @default.
- W3215726571 isParatext "false" @default.
- W3215726571 isRetracted "false" @default.
- W3215726571 magId "3215726571" @default.
- W3215726571 workType "article" @default.