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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.10035 |
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| _version_ | 1866913939838730240 |
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| author | Matsumoto, Jun |
| author_facet | Matsumoto, Jun |
| contents | We study a global theory of affine maximal surfaces with singularities, which are called affine maximal maps and defined by Aledo--Mart\' inez--Mil\' an. In this paper, we define a special subclass of such surfaces other than improper affine fronts, called \emph{affine maxfaces}, and investigate their global properties with respect to certain notions of completeness. In particular, by applying Euclidean minimal surface theory, we show that ``complete'' affine maxfaces satisfy an Osserman-type inequality. Moreover, one can also observe that affine maxfaces are in a class that does not contain non-trivial improper affine fronts. We also provide examples of such surfaces which are related to Euclidean minimal surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of affine maximal surfaces with singularities and its relationship with minimal surface theory Matsumoto, Jun Differential Geometry We study a global theory of affine maximal surfaces with singularities, which are called affine maximal maps and defined by Aledo--Mart\' inez--Mil\' an. In this paper, we define a special subclass of such surfaces other than improper affine fronts, called \emph{affine maxfaces}, and investigate their global properties with respect to certain notions of completeness. In particular, by applying Euclidean minimal surface theory, we show that ``complete'' affine maxfaces satisfy an Osserman-type inequality. Moreover, one can also observe that affine maxfaces are in a class that does not contain non-trivial improper affine fronts. We also provide examples of such surfaces which are related to Euclidean minimal surfaces. |
| title | A class of affine maximal surfaces with singularities and its relationship with minimal surface theory |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.10035 |