Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952481875> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W2952481875 abstract "Consider a 2-plane $P subset mathbb{C}^n$ and let $D$ be a bounded region in $P$ with a piecewise-smooth boundary. Let $I(D)$ be the infimum of areas of all piecewise-smooth isotropic surfaces in $mathbb{C}^n$ with the same boundary as $D$. Then $I(D)= lambda_P^n cdot Area(D)$. If $P$ is not complex, $lambda_P^n < frac{3pi}{2sqrt{2}}$. For a complex plane $mathbb{C} subset mathbb{C}^n$, $lambda_{mathbb{C}}^n geq 2$, $lambda_{mathbb{C}}^2 geq 3$ and also $frac{3pi^2}{2sqrt{2}}$ is the area of an explicit Hamiltonian stationary isotropic Mobius band embedded in $mathbb{C}^n$ whose boundary is a unit circle in $mathbb{C}$. As a corollary, a compact surface $Sigma$ (possibly with boundary) in a symplectic manifold can be approximated by isotropic surfaces of area $leq frac{3pi}{2sqrt{2}} Area(Sigma)$. Another corollary is that a closed curve of length $l$ in $mathbb{C}^n$ bounds an isotropic surface of area $leq frac{3l^2}{8sqrt{2}}$. A related result is the following: consider $mathbb{C}P^1 subset mathbb{C}P^n$ and let $D$ be a region in $mathbb{C}P^1$. Let $I(D)$ be the infimum of areas of all isotropic surfaces in $mathbb{C}P^n$ with the same boundary as $D$ representing the same relative homology class mod 2 as $D$. Then $ 2 cdot Area(D) leq I(D) leq lambda_{mathbb{C}}^n cdot Area(D)$. Moreover the first inequality becomes an equality for $D=mathbb{C}P^1$." @default.
- W2952481875 created "2019-06-27" @default.
- W2952481875 creator A5083776330 @default.
- W2952481875 date "2004-09-17" @default.
- W2952481875 modified "2023-09-27" @default.
- W2952481875 title "Area comparison results for isotropic surfaces" @default.
- W2952481875 cites W1903315566 @default.
- W2952481875 cites W2001716610 @default.
- W2952481875 cites W2047527454 @default.
- W2952481875 cites W2054612392 @default.
- W2952481875 cites W2062461628 @default.
- W2952481875 cites W2335223444 @default.
- W2952481875 cites W2799990588 @default.
- W2952481875 hasPublicationYear "2004" @default.
- W2952481875 type Work @default.
- W2952481875 sameAs 2952481875 @default.
- W2952481875 citedByCount "0" @default.
- W2952481875 crossrefType "posted-content" @default.
- W2952481875 hasAuthorship W2952481875A5083776330 @default.
- W2952481875 hasConcept C114614502 @default.
- W2952481875 hasConcept C121332964 @default.
- W2952481875 hasConcept C134306372 @default.
- W2952481875 hasConcept C184050105 @default.
- W2952481875 hasConcept C2524010 @default.
- W2952481875 hasConcept C2778113609 @default.
- W2952481875 hasConcept C33923547 @default.
- W2952481875 hasConcept C62354387 @default.
- W2952481875 hasConcept C62520636 @default.
- W2952481875 hasConcept C95611797 @default.
- W2952481875 hasConceptScore W2952481875C114614502 @default.
- W2952481875 hasConceptScore W2952481875C121332964 @default.
- W2952481875 hasConceptScore W2952481875C134306372 @default.
- W2952481875 hasConceptScore W2952481875C184050105 @default.
- W2952481875 hasConceptScore W2952481875C2524010 @default.
- W2952481875 hasConceptScore W2952481875C2778113609 @default.
- W2952481875 hasConceptScore W2952481875C33923547 @default.
- W2952481875 hasConceptScore W2952481875C62354387 @default.
- W2952481875 hasConceptScore W2952481875C62520636 @default.
- W2952481875 hasConceptScore W2952481875C95611797 @default.
- W2952481875 hasLocation W29524818751 @default.
- W2952481875 hasOpenAccess W2952481875 @default.
- W2952481875 hasPrimaryLocation W29524818751 @default.
- W2952481875 hasRelatedWork W2020689899 @default.
- W2952481875 hasRelatedWork W2072764770 @default.
- W2952481875 hasRelatedWork W2090491788 @default.
- W2952481875 hasRelatedWork W2100796162 @default.
- W2952481875 hasRelatedWork W2167025208 @default.
- W2952481875 hasRelatedWork W2739713617 @default.
- W2952481875 hasRelatedWork W2775234117 @default.
- W2952481875 hasRelatedWork W2787339217 @default.
- W2952481875 hasRelatedWork W2803583121 @default.
- W2952481875 hasRelatedWork W2919279005 @default.
- W2952481875 hasRelatedWork W2949431594 @default.
- W2952481875 hasRelatedWork W2963558003 @default.
- W2952481875 hasRelatedWork W2963889475 @default.
- W2952481875 hasRelatedWork W2964049553 @default.
- W2952481875 hasRelatedWork W2969375488 @default.
- W2952481875 hasRelatedWork W3098461411 @default.
- W2952481875 hasRelatedWork W3139002430 @default.
- W2952481875 hasRelatedWork W3181489674 @default.
- W2952481875 hasRelatedWork W3207571205 @default.
- W2952481875 hasRelatedWork W812236731 @default.
- W2952481875 isParatext "false" @default.
- W2952481875 isRetracted "false" @default.
- W2952481875 magId "2952481875" @default.
- W2952481875 workType "article" @default.