FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1996089287> ?p ?o ?g. }

• W1996089287 endingPage "506" @default.
• W1996089287 startingPage "489" @default.
• W1996089287 abstract "Suppose that $Sigma=partial M$ is the $n$-dimensional boundary of a connected compact Riemannian spin manifold $( M,langle;,;rangle)$ with non-negative scalar curvature, and that the (inward) mean curvature $H$ of $Sigma$ is positive. We show that the first eigenvalue of the Dirac operator of the boundary corresponding to the conformal metric $langle;,;rangle_H=H^2langle;,;rangle$ is at least $n/2$ and equality holds if and only if there exists a parallel spinor field on $ M$. As a consequence, if $Sigma$ admits an isometric and isospin immersion $phi$ with mean curvature $H_0$ as a hypersurface into another spin Riemannian manifold $ M_0$ admitting a parallel spinor field, then begin{equation} label{HoloIneq} int_Sigma H,dSigmale int_Sigma frac{H^2_0}{H}, dSigma end{equation} and equality holds if and only if both immersions have the same shape operator. In this case, $Sigma$ has to be also connected. In the special case where $M_0=R^{n+1}$, equality in (ref{HoloIneq}) implies that $M$ is an Euclidean domain and $phi$ is congruent to the embedding of $Sigma$ in $M$ as its boundary. We also prove that Inequality (ref{HoloIneq}) implies the Positive Mass Theorem (PMT). Note that, using the PMT and the additional assumption that $phi$ is a strictly convex embedding into the Euclidean space, Shi and Tam cite{ST1} proved the integral inequality begin{equation}label{shi-tam-Ineq} int_Sigma H,dSigmale int_Sigma H_0, dSigma, end{equation} which is stronger than (ref{HoloIneq}) ." @default.
• W1996089287 created "2016-06-24" @default.
• W1996089287 creator A5058687582 @default.
• W1996089287 creator A5076535190 @default.
• W1996089287 date "2014-01-01" @default.
• W1996089287 modified "2023-10-18" @default.
• W1996089287 title "A holographic principle for the existence of parallel spinor fields and an inequality of Shi-Tam type" @default.
• W1996089287 cites W1273306973 @default.
• W1996089287 cites W1498143011 @default.
• W1996089287 cites W1532154335 @default.
• W1996089287 cites W1545407008 @default.
• W1996089287 cites W1571962299 @default.
• W1996089287 cites W1789219287 @default.
• W1996089287 cites W1963526424 @default.
• W1996089287 cites W1982127738 @default.
• W1996089287 cites W1990005223 @default.
• W1996089287 cites W1993272741 @default.
• W1996089287 cites W2003202662 @default.
• W1996089287 cites W2011758747 @default.
• W1996089287 cites W2013506344 @default.
• W1996089287 cites W2015106666 @default.
• W1996089287 cites W2043574588 @default.
• W1996089287 cites W2045707359 @default.
• W1996089287 cites W2052871565 @default.
• W1996089287 cites W2075724583 @default.
• W1996089287 cites W2101310208 @default.
• W1996089287 cites W2105973581 @default.
• W1996089287 cites W2127494126 @default.
• W1996089287 cites W2139496359 @default.
• W1996089287 cites W2167167527 @default.
• W1996089287 cites W2167184126 @default.
• W1996089287 cites W2482762127 @default.
• W1996089287 cites W2729720141 @default.
• W1996089287 cites W2734711459 @default.
• W1996089287 cites W2791773610 @default.
• W1996089287 cites W2952660207 @default.
• W1996089287 cites W3100914057 @default.
• W1996089287 cites W3104922414 @default.
• W1996089287 cites W1630303706 @default.
• W1996089287 doi "https://doi.org/10.4310/ajm.2014.v18.n3.a6" @default.
• W1996089287 hasPublicationYear "2014" @default.
• W1996089287 type Work @default.
• W1996089287 sameAs 1996089287 @default.
• W1996089287 citedByCount "12" @default.
• W1996089287 countsByYear W19960892872014 @default.
• W1996089287 countsByYear W19960892872015 @default.
• W1996089287 countsByYear W19960892872017 @default.
• W1996089287 countsByYear W19960892872019 @default.
• W1996089287 countsByYear W19960892872020 @default.
• W1996089287 countsByYear W19960892872021 @default.
• W1996089287 countsByYear W19960892872022 @default.
• W1996089287 crossrefType "journal-article" @default.
• W1996089287 hasAuthorship W1996089287A5058687582 @default.
• W1996089287 hasAuthorship W1996089287A5076535190 @default.
• W1996089287 hasBestOaLocation W19960892871 @default.
• W1996089287 hasConcept C114614502 @default.
• W1996089287 hasConcept C12520029 @default.
• W1996089287 hasConcept C134306372 @default.
• W1996089287 hasConcept C195065555 @default.
• W1996089287 hasConcept C2524010 @default.
• W1996089287 hasConcept C2779593128 @default.
• W1996089287 hasConcept C33923547 @default.
• W1996089287 hasConcept C37914503 @default.
• W1996089287 hasConcept C43506125 @default.
• W1996089287 hasConceptScore W1996089287C114614502 @default.
• W1996089287 hasConceptScore W1996089287C12520029 @default.
• W1996089287 hasConceptScore W1996089287C134306372 @default.
• W1996089287 hasConceptScore W1996089287C195065555 @default.
• W1996089287 hasConceptScore W1996089287C2524010 @default.
• W1996089287 hasConceptScore W1996089287C2779593128 @default.
• W1996089287 hasConceptScore W1996089287C33923547 @default.
• W1996089287 hasConceptScore W1996089287C37914503 @default.
• W1996089287 hasConceptScore W1996089287C43506125 @default.
• W1996089287 hasIssue "3" @default.
• W1996089287 hasLocation W19960892871 @default.
• W1996089287 hasLocation W19960892872 @default.
• W1996089287 hasLocation W19960892873 @default.
• W1996089287 hasLocation W19960892874 @default.
• W1996089287 hasLocation W19960892875 @default.
• W1996089287 hasLocation W19960892876 @default.
• W1996089287 hasLocation W19960892877 @default.
• W1996089287 hasLocation W19960892878 @default.
• W1996089287 hasOpenAccess W1996089287 @default.
• W1996089287 hasPrimaryLocation W19960892871 @default.
• W1996089287 hasRelatedWork W1977484341 @default.
• W1996089287 hasRelatedWork W2000869778 @default.
• W1996089287 hasRelatedWork W2031110205 @default.
• W1996089287 hasRelatedWork W2047608647 @default.
• W1996089287 hasRelatedWork W2055518426 @default.
• W1996089287 hasRelatedWork W2070837384 @default.
• W1996089287 hasRelatedWork W2185621338 @default.
• W1996089287 hasRelatedWork W2962697612 @default.
• W1996089287 hasRelatedWork W2999390632 @default.
• W1996089287 hasRelatedWork W4381586607 @default.
• W1996089287 hasVolume "18" @default.
• W1996089287 isParatext "false" @default.
• W1996089287 isRetracted "false" @default.
• W1996089287 magId "1996089287" @default.

• next