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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.10044 |
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| _version_ | 1866912272792682496 |
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| author | Böröczky, Károly J. Kovács, Ágnes Mui, Stephanie Zhang, Gaoyong |
| author_facet | Böröczky, Károly J. Kovács, Ágnes Mui, Stephanie Zhang, Gaoyong |
| contents | This paper studies the general Lp dual curvature density equation under a group symmetry assumption. This geometric partial differential equation arises from the general Lp dual Minkowski problem of prescribing the Lp dual curvature measure of convex bodies. It is a Monge-Ampere type equation on the unit sphere. If the density function of the dual curvature measure is invariant under a closed subgroup of the orthogonal group, the geometric partial differential equation is solved in this paper for certain range of negative p using a variational method. This work generalizes recent results on the Lp dual Minkowski problem of origin-symmetric convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dual Curvature Density Equation with Group Symmetry Böröczky, Károly J. Kovács, Ágnes Mui, Stephanie Zhang, Gaoyong Analysis of PDEs This paper studies the general Lp dual curvature density equation under a group symmetry assumption. This geometric partial differential equation arises from the general Lp dual Minkowski problem of prescribing the Lp dual curvature measure of convex bodies. It is a Monge-Ampere type equation on the unit sphere. If the density function of the dual curvature measure is invariant under a closed subgroup of the orthogonal group, the geometric partial differential equation is solved in this paper for certain range of negative p using a variational method. This work generalizes recent results on the Lp dual Minkowski problem of origin-symmetric convex bodies. |
| title | Dual Curvature Density Equation with Group Symmetry |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.10044 |