The solvability of the L_p-dual mixed Euclidean-Gauss Minkowski problem

Abstract

This paper investigates the L_p-dual mixed Euclidean-Gauss Minkowski problem associated with the L_p-dual mixed Euclidean-Gaussian curvature measure. The solvability of this problem is equivalent to that of a class of Monge-Ampère type equations on the unit sphere. Under smooth assumptions, We establish the existence of solutions for p<1, q<0, and q<p and uniqueness of solutions for p≥ q to the aforementioned Monge-Ampère type equations, respectively. Furthermore, we obtain a complete solution concerning the existence part of this problem when p<1 and q<0.

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BibTeX RIS

BibTeX

@misc{fu2026solvability,
  title = {{The solvability of the $L_p$-dual mixed Euclidean-Gauss Minkowski problem}},
  author = {Na Fu and Jian-Ping Sun and Bin Chen and Ya-Hong Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23588},
  eprint = {2609.23588},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23588},
}

RIS

TY  - UNPB
TI  - The solvability of the L_p-dual mixed Euclidean-Gauss Minkowski problem
AU  - Na Fu
AU  - Jian-Ping Sun
AU  - Bin Chen
AU  - Ya-Hong Zhao
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23588
UR  - https://arxiv.org/abs/2609.23588
AB  - This paper investigates the L_p-dual mixed Euclidean-Gauss Minkowski problem associated with the L_p-dual mixed Euclidean-Gaussian curvature measure. The solvability of this problem is equivalent to that of a class of Monge-Ampère type equations on the unit sphere. Under smooth assumptions, We establish the existence of solutions for p<1, q<0, and q<p and uniqueness of solutions for p≥ q to the aforementioned Monge-Ampère type equations, respectively. Furthermore, we obtain a complete solution concerning the existence part of this problem when p<1 and q<0.
ER  -

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