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- Title
Evolution of geometric constant evolving along extended Ricci flow.
- Authors
Azami, Shahroud
- Abstract
We investigate the behavior of the lowest geometric constant, λ a , b c (g) , along the extended Ricci flow such that there exist positive solutions to the following partial differential equation: − Δ u + a u log u + b S c u = λ a , b c (g) u with ∫ M u 2 d μ = 1 , where a , b and c are real constants. We drive the evolution formula for the geometric constant λ a , b c (g) along the unnormalized and normalized extended Ricci flow. Moreover, we give some monotonic quantities involving λ a , b c (g) along the extended Ricci flow by imposing some geometric conditions.
- Subjects
RICCI flow; PARTIAL differential equations; MONOTONIC functions
- Publication
Asian-European Journal of Mathematics, 2023, Vol 16, Issue 5, p1
- ISSN
1793-5571
- Publication type
Article
- DOI
10.1142/S1793557123500900