The Journal of Geometric Analysis

, Volume 27, Issue 1, pp 409–441 | Cite as

BV Capacity on Generalized Grushin Plane



In this paper we introduce and investigate the so-called BV capacity on the generalized Grushin plane \(\mathbb {G}^2_\alpha \), thereby discovering some sharp trace and BV isocapacity inequalities on \(\mathbb {G}^2_\alpha \).


Isoperimetric inequality Sub-Riemannian manifolds  Grushin plane BV capacity 

Mathematics Subject Classification

32U20 53C17 



The author is greatly indebted to the referees for their very careful reading and many valuable comments on this paper. The author would like to thank Prof. Jie Xiao for his constructive suggestions and providing his manuscript on this subject. Moreover, the author would like to thank the Department of Mathematics and Statistics at Memorial University of Newfoundland for its hospitality. The author is supported by the National Natural Science Foundation of China (Nos. 10901018, 11471018), the Fundamental Research Funds for the Central Universities (No. FRF-TP-14-005C1), Program for New Century Excellent Talents in University and the Beijing Natural Science Foundation under Grant (No. 1142005).


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Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina

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