The Lp chord Minkowski problem
Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the Lp{L}_{p} chord measures is c...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-01-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2022-0041 |
| _version_ | 1811171860792999936 |
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| author | Xi Dongmeng Yang Deane Zhang Gaoyong Zhao Yiming |
| author_facet | Xi Dongmeng Yang Deane Zhang Gaoyong Zhao Yiming |
| author_sort | Xi Dongmeng |
| collection | DOAJ |
| description | Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the Lp{L}_{p} chord measures is called the Lp{L}_{p} chord Minkowski problem in the Lp{L}_{p} Brunn-Minkowski theory, which includes the Lp{L}_{p} Minkowski problem as a special case. This article solves the Lp{L}_{p} chord Minkowski problem when p>1p\gt 1 and the symmetric case of 0<p<10\lt p\lt 1. |
| first_indexed | 2024-04-10T17:22:18Z |
| format | Article |
| id | doaj.art-0fc176d040524ede90edd5979b7dc829 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-10T17:22:18Z |
| publishDate | 2023-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-0fc176d040524ede90edd5979b7dc8292023-02-05T08:43:35ZengDe GruyterAdvanced Nonlinear Studies2169-03752023-01-0123190794510.1515/ans-2022-0041The Lp chord Minkowski problemXi Dongmeng0Yang Deane1Zhang Gaoyong2Zhao Yiming3Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USADepartment of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USADepartment of Mathematics, Syracuse University, Syracuse, NY 13244, USAChord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the Lp{L}_{p} chord measures is called the Lp{L}_{p} chord Minkowski problem in the Lp{L}_{p} Brunn-Minkowski theory, which includes the Lp{L}_{p} Minkowski problem as a special case. This article solves the Lp{L}_{p} chord Minkowski problem when p>1p\gt 1 and the symmetric case of 0<p<10\lt p\lt 1.https://doi.org/10.1515/ans-2022-0041chord integralchord measurelp surface area measurelp chord measurelp minkowski problemlp chord minkowski problem52a38 |
| spellingShingle | Xi Dongmeng Yang Deane Zhang Gaoyong Zhao Yiming The Lp chord Minkowski problem Advanced Nonlinear Studies chord integral chord measure lp surface area measure lp chord measure lp minkowski problem lp chord minkowski problem 52a38 |
| title | The Lp chord Minkowski problem |
| title_full | The Lp chord Minkowski problem |
| title_fullStr | The Lp chord Minkowski problem |
| title_full_unstemmed | The Lp chord Minkowski problem |
| title_short | The Lp chord Minkowski problem |
| title_sort | lp chord minkowski problem |
| topic | chord integral chord measure lp surface area measure lp chord measure lp minkowski problem lp chord minkowski problem 52a38 |
| url | https://doi.org/10.1515/ans-2022-0041 |
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