The Sobolev inequalities along the Ricci-Bourguignon flow and applications

Mehdi Jafari; Shahroud Azami; U.c. De

doi:10.15672/hujms.1618538

The Sobolev inequalities along the Ricci-Bourguignon flow and applications

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, ‎it confidently investigates the $\kappa$-noncollapsing‎ ‎estimates along the RBF‎.

Keywords

References

1] A. Abolarinwa, Sobolev-type inequalities and heat kernel bounds along the geometric flow, Afr. Math. 27, 169–186, 2016.

Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Mehdi Jafari ^*
0000-0002-7154-7527
Iran

Shahroud Azami
0000-0002-8976-2014
Iran

U.c. De
0000-0002-8990-4609
India

Early Pub Date

August 17, 2026

Publication Date

-

Submission Date

January 12, 2025

Acceptance Date

April 16, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.15672/hujms.1618538

IZ

https://izlik.org/JA45CD93NH

Cite

RIS / Bibtex

APA

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

AMA

1.Jafari M, Azami S, De U. The Sobolev inequalities along the Ricci-Bourguignon flow and applications. Hacettepe Journal of Mathematics and Statistics. 2026;(Advanced Online Publication). doi:10.15672/hujms.1618538

Chicago

Jafari, Mehdi, Shahroud Azami, and U.c. De. 2026. “The Sobolev Inequalities Along the Ricci-Bourguignon Flow and Applications”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication. https://doi.org/10.15672/hujms.1618538.

EndNote

Jafari M, Azami S, De U (August 1, 2026) The Sobolev inequalities along the Ricci-Bourguignon flow and applications. Hacettepe Journal of Mathematics and Statistics Advanced Online Publication

IEEE

[1]M. Jafari, S. Azami, and U. De, “The Sobolev inequalities along the Ricci-Bourguignon flow and applications”, Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Aug. 2026, doi: 10.15672/hujms.1618538.

ISNAD

Jafari, Mehdi - Azami, Shahroud - De, U.c. “The Sobolev Inequalities Along the Ricci-Bourguignon Flow and Applications”. Hacettepe Journal of Mathematics and Statistics. Advanced Online Publication (August 1, 2026). https://doi.org/10.15672/hujms.1618538.

JAMA

1.Jafari M, Azami S, De U. The Sobolev inequalities along the Ricci-Bourguignon flow and applications. Hacettepe Journal of Mathematics and Statistics. 2026. doi:10.15672/hujms.1618538.

MLA

Jafari, Mehdi, et al. “The Sobolev Inequalities Along the Ricci-Bourguignon Flow and Applications”. Hacettepe Journal of Mathematics and Statistics, no. Advanced Online Publication, Aug. 2026, doi:10.15672/hujms.1618538.

Vancouver

1.Mehdi Jafari, Shahroud Azami, U.c. De. The Sobolev inequalities along the Ricci-Bourguignon flow and applications. Hacettepe Journal of Mathematics and Statistics. 2026 Aug. 1;(Advanced Online Publication). doi:10.15672/hujms.1618538