Critical, stability and higher-order analysis for Hardy type inequalities on Cartan–Hadamard manifolds
Roychowdhury P. Suragan D. Yessirkegenov N.
November 2025Springer Science and Business Media Deutschland GmbH
Mathematische Zeitschrift
2025#311Issue 3
In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan–Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance. Secondly, we examine the stability of both critical and subcriwtical cases of the Hardy inequality. Lastly, we establish two weighted Hardy-type inequalities where singularities appear at the origin as well as the boundary, and we discuss their implications for higher-order operators. Our results improve upon previous findings and also present new higher-order versions of these inequalities as additional outcomes.
Cartan–Hadamard manifolds , Hardy inequality , Rellich inequality , Sharp constant , Stability of inequality
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Kerala School of Mathematics, Kerala, Calicut (Kozhikode), 673571, India
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
KIMEP University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kerala School of Mathematics
Department of Mathematics
KIMEP University
Institute of Mathematics and Mathematical Modeling
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