Prescribed $T$-curvature flow on the four-dimensional unit ball
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917234924847104 |
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| author | Ho, Pak Tung Ndiaye, Cheikh Birahim Sun, Liming Wang, Heming |
| author_facet | Ho, Pak Tung Ndiaye, Cheikh Birahim Sun, Liming Wang, Heming |
| contents | In this paper, we study the prescribed $T$-curvature problem on the unit ball $\mathbb{B}^4$ of $\mathbb{R} ^4$ via the $T$-curvature flow approach. By combining Ache-Chang's inequality with the Morse-theoretic approach of Malchiodi-Struwe, we establish existence results under strong Morse-type inequalities at infinity. As a byproduct of our argument, we also prove the exponential convergence of the $T$-curvature flow on $\mathbb{B}^4$, starting from a $Q$-flat and minimal metric conformal to the standard Euclidean metric, to an extremal metric of Ache-Chang's inequality whose explicit expression was derived by Ndiaye-Sun. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prescribed $T$-curvature flow on the four-dimensional unit ball Ho, Pak Tung Ndiaye, Cheikh Birahim Sun, Liming Wang, Heming Differential Geometry Analysis of PDEs Primary 35B33, 35J35. Secondary 53C21 In this paper, we study the prescribed $T$-curvature problem on the unit ball $\mathbb{B}^4$ of $\mathbb{R} ^4$ via the $T$-curvature flow approach. By combining Ache-Chang's inequality with the Morse-theoretic approach of Malchiodi-Struwe, we establish existence results under strong Morse-type inequalities at infinity. As a byproduct of our argument, we also prove the exponential convergence of the $T$-curvature flow on $\mathbb{B}^4$, starting from a $Q$-flat and minimal metric conformal to the standard Euclidean metric, to an extremal metric of Ache-Chang's inequality whose explicit expression was derived by Ndiaye-Sun. |
| title | Prescribed $T$-curvature flow on the four-dimensional unit ball |
| topic | Differential Geometry Analysis of PDEs Primary 35B33, 35J35. Secondary 53C21 |
| url | https://arxiv.org/abs/2601.22934 |