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Singular Moser-Trudinger inequality with the exact growth condition on hyperbolic space
1School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University, Nanchang, 330038 China.
Journal of Inequalities and Applications
|July 7, 2017
Summary
This study establishes a singular Moser-Trudinger inequality in n-dimension hyperbolic space, extending prior research on inequalities with exact growth conditions.
Area of Science:
- Geometric analysis
- Inequalities
- Hyperbolic geometry
Background:
- The Moser-Trudinger inequality is a fundamental result in analysis.
- Previous work established related inequalities in various spaces.
- Singular versions of inequalities are crucial for understanding function spaces.
Purpose of the Study:
- To investigate a singular version of the Moser-Trudinger inequality.
- To establish the exact growth condition for this inequality.
- To analyze the inequality within the n-dimension hyperbolic space.
Main Methods:
- Utilizing techniques from geometric analysis.
- Applying methods for establishing sharp inequalities.
- Adapting existing frameworks to the hyperbolic setting.
Main Results:
- A novel singular Moser-Trudinger inequality is proven.
- The exact growth condition is identified for the n-dimension hyperbolic space.
- The result extends the findings of Lu and Tang (2016).
Conclusions:
- The established inequality provides a new tool in geometric analysis.
- This work contributes to the understanding of sharp inequalities in non-Euclidean spaces.
- The findings open avenues for further research in hyperbolic geometry and analysis.
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