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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 5

The Sobolev inequalities along the Ricci-Bourguignon flow and applications

Mehdi Jafari(payame Noor university)0000-0002-7154-7527
Shahroud Azami(‎Imam Khomeini International University)0000-0002-8976-2014
U.c. De(‎University of Calcutta)0000-0002-8990-4609
Sayfa
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Yayın Tarihi
2026-10-28
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Additionally, {this paper investigates} the $\kappa$-noncollapsing estimates along the RBF.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Consider a closed Riemannian manifold $M$ where the metrics $g(t)$ evolve by the Ricci-Bourguignon flow (RBF).The paper first derives a Sobolev inequality along the RBF.
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Temel Bulgular & Veri:Then, by applying this Sobolev inequality we obtain a linear parabolic estimate and an upper bound estimate for the heat kernel along the RBF.
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Sonuç & Katkı:Additionally, {this paper investigates} the $\kappa$-noncollapsing estimates along the RBF.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ricci-Bourguignon flow · eigenvalue · monotonicity formula

Abstract

Consider a closed Riemannian manifold $M$ where the metrics $g(t)$ evolve by the Ricci-Bourguignon flow (RBF).The paper first derives a Sobolev inequality along the RBF. Then, by applying this Sobolev inequality we obtain a linear parabolic estimate and an upper bound estimate for the heat kernel along the RBF. Additionally, {this paper investigates} the $\kappa$-noncollapsing estimates along the RBF.

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Bu Makaleye Atıf Yap

Jafari, M., Azami, S., De, U. (2026). The Sobolev inequalities along the Ricci-Bourguignon flow and applications. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 5. https://doi.org/10.15672/hujms.1618538

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