Convex and quasiconvex truncations of nonconvex functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908865169195008 |
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| author | Pintea, Cornel |
| author_facet | Pintea, Cornel |
| contents | We consider nonconvex real valued functions whose truncations are either quasiconvex or even convex starting with a certain level. Among them, the $C^2$-smooth functions whose level sets are all completely contained in the positive definite region of their Hessian matrices, starting with a certain level, are good examples of such functions. For such a function we show the injectivity of its restricted gradient to a large subset of the positive definite region of its Hessian matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex and quasiconvex truncations of nonconvex functions Pintea, Cornel Classical Analysis and ODEs Differential Geometry We consider nonconvex real valued functions whose truncations are either quasiconvex or even convex starting with a certain level. Among them, the $C^2$-smooth functions whose level sets are all completely contained in the positive definite region of their Hessian matrices, starting with a certain level, are good examples of such functions. For such a function we show the injectivity of its restricted gradient to a large subset of the positive definite region of its Hessian matrices. |
| title | Convex and quasiconvex truncations of nonconvex functions |
| topic | Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2603.03516 |