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  • S pomocí Feffermanova klasického výsledku o hraniční singularitě Bergmanova jádra je odvozen analogický popis hraničního chování různých souvisejících veličin, jako Bergmanova invariantu, koeficientů Bergmanovy metriky, asociovaného Laplaceova-Beltramiho operátoru, jejího tenzoru křivosti, Ricciho tenzoru a skalární křivosti. Třebaže by se daly očekávat - díky derivacím které vstupují do jejich definic - u těchto veličin singularity o něco silnější než má Bergmanovo jádro, ukazuje se, že vesměs mají - až na rozdílné mocniny definující funkce oblasti v hlavních členech - tentýž typ singularity jako řešení Monge-Ampérovy rovnice. (cs)
  • Using Fefferman´s classical result on the boundary singularity of the Bergman kernel, we give an analogous description of the boundary behaviour of various related quantities like the Bergman invariant, the coefficients of the Bergman metric, of the associated Laplace-Beltrami operator, of its curvature tensor, Ricci curvature and scalar curvature. The main point is that even though one would expect a bit stronger singularities than the one for the Bergman kernel, due to the differentiations involved, all these quantities turn out to have - except for a different leading power of the defining function - the same kind of singularity as the solution of the Monge-Ampére equation.
  • Using Fefferman´s classical result on the boundary singularity of the Bergman kernel, we give an analogous description of the boundary behaviour of various related quantities like the Bergman invariant, the coefficients of the Bergman metric, of the associated Laplace-Beltrami operator, of its curvature tensor, Ricci curvature and scalar curvature. The main point is that even though one would expect a bit stronger singularities than the one for the Bergman kernel, due to the differentiations involved, all these quantities turn out to have - except for a different leading power of the defining function - the same kind of singularity as the solution of the Monge-Ampére equation. (en)
Title
  • Boundary behaviour of the Bergman invariant and related quantities
  • Boundary behaviour of the Bergman invariant and related quantities (en)
  • Hraniční chování Bergmanova jádra a souvisejících veličin (cs)
skos:prefLabel
  • Boundary behaviour of the Bergman invariant and related quantities
  • Boundary behaviour of the Bergman invariant and related quantities (en)
  • Hraniční chování Bergmanova jádra a souvisejících veličin (cs)
skos:notation
  • RIV/47813059:19610/08:#0000201!RIV08-MSM-19610___
http://linked.open.../vavai/riv/strany
  • 19;37
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika
  • 1
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http://linked.open...aciTvurceVysledku
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http://linked.open...titaPredkladatele
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  • 358415
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  • RIV/47813059:19610/08:#0000201
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  • Bergman kernel; Bergman invariant; Bergman metric (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • AT - Rakouská republika
http://linked.open...ontrolniKodProRIV
  • [5C056FD6CED2]
http://linked.open...i/riv/nazevZdroje
  • Monatshefte für Mathematik
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 154
http://linked.open...iv/tvurceVysledku
  • Engliš, Miroslav
http://linked.open...n/vavai/riv/zamer
issn
  • 0026-9255
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  • 19610
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