Matches in SemOpenAlex for { <https://semopenalex.org/work/W2915756083> ?p ?o ?g. }
Showing items 1 to 95 of
95
with 100 items per page.
- W2915756083 abstract "Let $Msubset mathbb{S}^{n+1}subsetmathbb{R}^{n+2}$ be a compact cmc rotational hypersurface of the $(n+1)$-dimensional Euclidean unit sphere. Denote by $|A|^2$ the square of the norm of the second fundamental form and $J(f)=-Delta f-nf-|A|^2f$ the stability or Jacobi operator. In this paper we compute the spectra of their Laplace and Jacobi operators in terms of eigenvalues of second order Hill's equations. For the minimal rotational examples, we prove that the stability index --the numbers of negative eigenvalues of the Jacobi operator counted with multiplicity -- is greater than $3 n+4$ and we also prove that there are at least 2 positive eigenvalues of the Laplacian of $M$ smaller than $n$. When $H$ is not zero, we have that every non-flat CMC rotational immersion is generated by rotating a planar profile curve along a geodesic called the axis of rotation. Let $m$ be the number of points where the maximal distance from this profile curve to the origin is achieved (we assume that the coordinates of the plane containing the profile curve has been set up so that the axis of rotation goes through the origin). Let $l$ be be the wrapping number of the profile curve. We show that the number of negative eigenvalues of the operator $J$ counted with multiplicity is at least $(2l-1)n+(2m-1)$. This result was proven for the case $n=2$ by Rossman and Sultana. They called $m$ the number of bulges or the number of necks. We will slightly change the definition of $l$ to include immersed examples that contain the axis of rotation." @default.
- W2915756083 created "2019-03-02" @default.
- W2915756083 creator A5024135704 @default.
- W2915756083 date "2019-02-19" @default.
- W2915756083 modified "2023-10-18" @default.
- W2915756083 title "Spectrum of the Laplacian and the Jacobi operator on rotational cmc hypersurfaces of spheres" @default.
- W2915756083 cites W1531608165 @default.
- W2915756083 cites W1590997457 @default.
- W2915756083 cites W1701933166 @default.
- W2915756083 cites W1996314429 @default.
- W2915756083 cites W1998542070 @default.
- W2915756083 cites W2070166786 @default.
- W2915756083 cites W2125507914 @default.
- W2915756083 cites W2321095540 @default.
- W2915756083 cites W2321377576 @default.
- W2915756083 cites W2729975235 @default.
- W2915756083 cites W2963207260 @default.
- W2915756083 cites W2963618607 @default.
- W2915756083 hasPublicationYear "2019" @default.
- W2915756083 type Work @default.
- W2915756083 sameAs 2915756083 @default.
- W2915756083 citedByCount "0" @default.
- W2915756083 crossrefType "posted-content" @default.
- W2915756083 hasAuthorship W2915756083A5024135704 @default.
- W2915756083 hasConcept C104317684 @default.
- W2915756083 hasConcept C10628310 @default.
- W2915756083 hasConcept C114410712 @default.
- W2915756083 hasConcept C114614502 @default.
- W2915756083 hasConcept C121332964 @default.
- W2915756083 hasConcept C129782007 @default.
- W2915756083 hasConcept C134306372 @default.
- W2915756083 hasConcept C156004811 @default.
- W2915756083 hasConcept C156778621 @default.
- W2915756083 hasConcept C158448853 @default.
- W2915756083 hasConcept C158693339 @default.
- W2915756083 hasConcept C165700671 @default.
- W2915756083 hasConcept C165818556 @default.
- W2915756083 hasConcept C17020691 @default.
- W2915756083 hasConcept C185592680 @default.
- W2915756083 hasConcept C2524010 @default.
- W2915756083 hasConcept C33923547 @default.
- W2915756083 hasConcept C48490523 @default.
- W2915756083 hasConcept C55493867 @default.
- W2915756083 hasConcept C62520636 @default.
- W2915756083 hasConcept C633612 @default.
- W2915756083 hasConcept C86339819 @default.
- W2915756083 hasConceptScore W2915756083C104317684 @default.
- W2915756083 hasConceptScore W2915756083C10628310 @default.
- W2915756083 hasConceptScore W2915756083C114410712 @default.
- W2915756083 hasConceptScore W2915756083C114614502 @default.
- W2915756083 hasConceptScore W2915756083C121332964 @default.
- W2915756083 hasConceptScore W2915756083C129782007 @default.
- W2915756083 hasConceptScore W2915756083C134306372 @default.
- W2915756083 hasConceptScore W2915756083C156004811 @default.
- W2915756083 hasConceptScore W2915756083C156778621 @default.
- W2915756083 hasConceptScore W2915756083C158448853 @default.
- W2915756083 hasConceptScore W2915756083C158693339 @default.
- W2915756083 hasConceptScore W2915756083C165700671 @default.
- W2915756083 hasConceptScore W2915756083C165818556 @default.
- W2915756083 hasConceptScore W2915756083C17020691 @default.
- W2915756083 hasConceptScore W2915756083C185592680 @default.
- W2915756083 hasConceptScore W2915756083C2524010 @default.
- W2915756083 hasConceptScore W2915756083C33923547 @default.
- W2915756083 hasConceptScore W2915756083C48490523 @default.
- W2915756083 hasConceptScore W2915756083C55493867 @default.
- W2915756083 hasConceptScore W2915756083C62520636 @default.
- W2915756083 hasConceptScore W2915756083C633612 @default.
- W2915756083 hasConceptScore W2915756083C86339819 @default.
- W2915756083 hasLocation W29157560831 @default.
- W2915756083 hasOpenAccess W2915756083 @default.
- W2915756083 hasPrimaryLocation W29157560831 @default.
- W2915756083 hasRelatedWork W1040578827 @default.
- W2915756083 hasRelatedWork W1575546529 @default.
- W2915756083 hasRelatedWork W1604759550 @default.
- W2915756083 hasRelatedWork W1930064044 @default.
- W2915756083 hasRelatedWork W1986840120 @default.
- W2915756083 hasRelatedWork W1999910175 @default.
- W2915756083 hasRelatedWork W2014479952 @default.
- W2915756083 hasRelatedWork W2017402340 @default.
- W2915756083 hasRelatedWork W2071788826 @default.
- W2915756083 hasRelatedWork W2094222716 @default.
- W2915756083 hasRelatedWork W2126982345 @default.
- W2915756083 hasRelatedWork W2604172172 @default.
- W2915756083 hasRelatedWork W2739240281 @default.
- W2915756083 hasRelatedWork W2768411919 @default.
- W2915756083 hasRelatedWork W2950983924 @default.
- W2915756083 hasRelatedWork W2951928139 @default.
- W2915756083 hasRelatedWork W3099566776 @default.
- W2915756083 hasRelatedWork W3111135550 @default.
- W2915756083 hasRelatedWork W3124567629 @default.
- W2915756083 hasRelatedWork W1857346485 @default.
- W2915756083 isParatext "false" @default.
- W2915756083 isRetracted "false" @default.
- W2915756083 magId "2915756083" @default.
- W2915756083 workType "article" @default.