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Smooth Yamabe invariant with boundary

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Abstract

In this paper, we study the smooth Yamabe invariant with boundary, which is defined to be the supremum of all the Yamabe constants on a manifold with boundary. We also study the problem of prescribing curvatures on manifolds with boundary under the condition of unit volume.

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Acknowledgements

We would like to thank the referee for his/her comments and suggestions which improve the presentation of this paper and make this paper more readable. The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2020R1A6A1A03047877 and 2019R1F1A1041021) and by the Korea Institute for Advanced Study (KIAS) grant funded by the Korean Government (MSIP). The second author was supported by a KIAS Individual Grant (MG070701) at Korea Institute for Advanced Study.

Funding

The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2020R1A6A1A03047877 and 2019R1F1A1041021) and by the Korea Institute for Advanced Study (KIAS) grant funded by the Korean Government (MSIP). The second author was supported by a KIAS Individual Grant (MG070701) at Korea Institute for Advanced Study.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 04107, Korea

    Pak Tung Ho

  2. Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Korea

    Pak Tung Ho & **woo Shin

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  1. Pak Tung Ho
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  2. **woo Shin
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Correspondence to **woo Shin.

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Ho, P.T., Shin, J. Smooth Yamabe invariant with boundary. Ann Glob Anal Geom 62, 413–435 (2022). https://doi.org/10.1007/s10455-022-09857-x

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