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A Polyakov Formula ...
A Polyakov Formula for Sectors
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- Aldana, C. L. (författare)
- Université du Luxembourg,University of Luxembourg
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- Rowlett, Julie, 1978 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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(creator_code:org_t)
- 2017-07-05
- 2018
- Engelska.
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Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 28:2, s. 1773-1839
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Abstract
Ämnesord
Stäng
- We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw-Sommerfeld's heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Polyakov formula
- Zeta-regularized determinant
- Sector
- Conical singularity
- Angular variation
- quantum geometry
- zeta-function
- ricci flow
- surfaces
- determinants
- laplacian
- manifolds
- heat
- cone
- strings
- Mathematics
- Sector
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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