Matches in SemOpenAlex for { <https://semopenalex.org/work/W3196367013> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W3196367013 endingPage "439" @default.
- W3196367013 startingPage "299" @default.
- W3196367013 abstract "In Part I of this article we generalize the Linearized Doubling (LD) approach, introduced in earlier work by NK, by proving a general theorem stating that if $Sigma$ is a closed minimal surface embedded in a Riemannian three-manifold $(N,g)$ and its Jacobi operator $mathcal{L}_Sigma$ has trivial kernel, then given a suitable family of LD solutions on $Sigma$, a minimal surface resembling two copies of $Sigma$ joined by many small catenoidal bridges can be constructed by PDE gluing methods. (An LD solution $varphi$ on $Sigma$ is a singular solution of the linear equation $mathcal{L}_Sigma varphi =0$ with logarithmic singularities; in the construction the singularities are replaced by catenoidal bridges.) As an example demonstrating the applicability of the theorem we construct new doublings of the Clifford torus. In Part II we construct families of LD solutions for general $(O(2)times Z_2)$-symmetric backgrounds $(Sigma, N,g)$. Combining with the theorem in Part I this implies the construction of new minimal doublings for such backgrounds. (Constructions for general backgrounds remain open.) This generalizes our earlier work for $Sigma=Sph^2 subset N=Sph^3$ providing new constructions even for that background. In Part III, applying the earlier result -- appropriately modified for the catenoid and the critical catenoid -- we construct new self-shrinkers of the mean curvature flow via doubling the spherical self-shrinker or the Angenent torus, new complete embedded minimal surfaces of finite total curvature in the Euclidean three-space via doubling the catenoid, and new free boundary minimal surfaces in the unit ball via doubling the critical catenoid." @default.
- W3196367013 created "2021-09-13" @default.
- W3196367013 creator A5082085878 @default.
- W3196367013 creator A5085297175 @default.
- W3196367013 date "2023-01-01" @default.
- W3196367013 modified "2023-09-27" @default.
- W3196367013 title "Generalizing the Linearized Doubling approach, I: General theory and new minimal surfaces and self-shrinkers" @default.
- W3196367013 cites W1479692803 @default.
- W3196367013 cites W1488778760 @default.
- W3196367013 cites W1491821783 @default.
- W3196367013 cites W1492904907 @default.
- W3196367013 cites W1541707047 @default.
- W3196367013 cites W1558378494 @default.
- W3196367013 cites W1606260297 @default.
- W3196367013 cites W1616916263 @default.
- W3196367013 cites W1823016041 @default.
- W3196367013 cites W1866311589 @default.
- W3196367013 cites W1976800439 @default.
- W3196367013 cites W2001180429 @default.
- W3196367013 cites W2003062603 @default.
- W3196367013 cites W2004659135 @default.
- W3196367013 cites W2048529987 @default.
- W3196367013 cites W2081706941 @default.
- W3196367013 cites W2137899790 @default.
- W3196367013 cites W2144913525 @default.
- W3196367013 cites W2148749808 @default.
- W3196367013 cites W2151764409 @default.
- W3196367013 cites W2318017669 @default.
- W3196367013 cites W2325240636 @default.
- W3196367013 cites W2330098160 @default.
- W3196367013 cites W2735517361 @default.
- W3196367013 cites W2759107740 @default.
- W3196367013 cites W2766277823 @default.
- W3196367013 cites W2810715698 @default.
- W3196367013 cites W2901379729 @default.
- W3196367013 cites W2962777874 @default.
- W3196367013 cites W2962964092 @default.
- W3196367013 cites W2963901840 @default.
- W3196367013 cites W2964014235 @default.
- W3196367013 cites W2964157365 @default.
- W3196367013 cites W2964309421 @default.
- W3196367013 cites W3093449924 @default.
- W3196367013 cites W3098183438 @default.
- W3196367013 cites W3099993333 @default.
- W3196367013 cites W3101844582 @default.
- W3196367013 cites W3104281714 @default.
- W3196367013 cites W3105289155 @default.
- W3196367013 cites W3105435868 @default.
- W3196367013 cites W3134740048 @default.
- W3196367013 cites W3154690435 @default.
- W3196367013 doi "https://doi.org/10.4310/cjm.2023.v11.n2.a1" @default.
- W3196367013 hasPublicationYear "2023" @default.
- W3196367013 type Work @default.
- W3196367013 sameAs 3196367013 @default.
- W3196367013 citedByCount "1" @default.
- W3196367013 countsByYear W31963670132019 @default.
- W3196367013 crossrefType "journal-article" @default.
- W3196367013 hasAuthorship W3196367013A5082085878 @default.
- W3196367013 hasAuthorship W3196367013A5085297175 @default.
- W3196367013 hasConcept C144237770 @default.
- W3196367013 hasConcept C199343813 @default.
- W3196367013 hasConcept C2777686260 @default.
- W3196367013 hasConcept C28826006 @default.
- W3196367013 hasConcept C33923547 @default.
- W3196367013 hasConcept C71924100 @default.
- W3196367013 hasConceptScore W3196367013C144237770 @default.
- W3196367013 hasConceptScore W3196367013C199343813 @default.
- W3196367013 hasConceptScore W3196367013C2777686260 @default.
- W3196367013 hasConceptScore W3196367013C28826006 @default.
- W3196367013 hasConceptScore W3196367013C33923547 @default.
- W3196367013 hasConceptScore W3196367013C71924100 @default.
- W3196367013 hasIssue "2" @default.
- W3196367013 hasLocation W31963670131 @default.
- W3196367013 hasOpenAccess W3196367013 @default.
- W3196367013 hasPrimaryLocation W31963670131 @default.
- W3196367013 hasRelatedWork W1993700123 @default.
- W3196367013 hasRelatedWork W1994109492 @default.
- W3196367013 hasRelatedWork W2063488590 @default.
- W3196367013 hasRelatedWork W2089811522 @default.
- W3196367013 hasRelatedWork W2094362282 @default.
- W3196367013 hasRelatedWork W2351859806 @default.
- W3196367013 hasRelatedWork W4205135043 @default.
- W3196367013 hasRelatedWork W4230623537 @default.
- W3196367013 hasRelatedWork W4230638242 @default.
- W3196367013 hasRelatedWork W4239376463 @default.
- W3196367013 hasVolume "11" @default.
- W3196367013 isParatext "false" @default.
- W3196367013 isRetracted "false" @default.
- W3196367013 magId "3196367013" @default.
- W3196367013 workType "article" @default.