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Capacity of a Condenser in the Heisenberg Group

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Abstract

We give new estimates on the capacity of a condenser in the first Heisenberg group. As an application, we establish new lower and upper bounds for the first eigenvalue of the Kohn–Laplace operator for a regular bounded open domain of the Heisenberg group.

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Acknowledgements

The authors would like to thank P. Pansu for his suggestions and advice.

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Authors and Affiliations

  1. College of Sciences, Taibah University, Medina, Saudi Arabia

    Najoua Gamara

  2. Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia

    Najoua Gamara & Akram Makni

Authors
  1. Najoua Gamara
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  2. Akram Makni
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Corresponding author

Correspondence to Najoua Gamara.

Additional information

Communicated by Norhashidah Hj. Mohd. Ali.

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Gamara, N., Makni, A. Capacity of a Condenser in the Heisenberg Group. Bull. Malays. Math. Sci. Soc. 42, 2739–2757 (2019). https://doi.org/10.1007/s40840-018-0628-7

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  • DOI: https://doi.org/10.1007/s40840-018-0628-7

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