Bounds on the dimension of lineal extensions
Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\...
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| creator | Bushling, Ryan E. G Fiedler, Jacob B |
| description | Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq
\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$
to a full line. Keleti's line segment extension conjecture posits that the
Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$,
we use effective methods to prove a strong packing dimension variant of this
conjecture, from which the generalized Kakeya conjecture for packing dimension
immediately follows. This is followed by several doubling estimates in higher
dimensions and connections to related problems. |
| doi_str_mv | 10.48550/arxiv.2404.16315 |
| format | Article |
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\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$
to a full line. Keleti's line segment extension conjecture posits that the
Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$,
we use effective methods to prove a strong packing dimension variant of this
conjecture, from which the generalized Kakeya conjecture for packing dimension
immediately follows. This is followed by several doubling estimates in higher
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\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$
to a full line. Keleti's line segment extension conjecture posits that the
Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$,
we use effective methods to prove a strong packing dimension variant of this
conjecture, from which the generalized Kakeya conjecture for packing dimension
immediately follows. This is followed by several doubling estimates in higher
dimensions and connections to related problems.</description><subject>Mathematics - Classical Analysis and ODEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzstOwzAQBVBvWKCWD2CFP6AJdsbPJVS8pEpsuo-mnrFqKQ-UBFT-HmhZXd27uDpC3GpVm2CtusfpVL7qxihTawfaXovN4_g50CzHQS5HllR6Huby28YsuzIwdpJPy2Wb1-IqYzfzzX-uxP75ab99rXbvL2_bh12FztsqIhlOWqXo4gE8NBQMJe8jUIgOMKVAaFlnhw4ZrPYu50CJGusUAcNK3F1uz9z2Yyo9Tt_tH7s9s-EHIr88-w</recordid><startdate>20240424</startdate><enddate>20240424</enddate><creator>Bushling, Ryan E. G</creator><creator>Fiedler, Jacob B</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240424</creationdate><title>Bounds on the dimension of lineal extensions</title><author>Bushling, Ryan E. G ; Fiedler, Jacob B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-9ad4ec10c969b3732d84dc7793d8963acc8da5e1f6a6ae35176ff8dcd2560d3e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Bushling, Ryan E. G</creatorcontrib><creatorcontrib>Fiedler, Jacob B</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bushling, Ryan E. G</au><au>Fiedler, Jacob B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bounds on the dimension of lineal extensions</atitle><date>2024-04-24</date><risdate>2024</risdate><abstract>Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq
\mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$
to a full line. Keleti's line segment extension conjecture posits that the
Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$,
we use effective methods to prove a strong packing dimension variant of this
conjecture, from which the generalized Kakeya conjecture for packing dimension
immediately follows. This is followed by several doubling estimates in higher
dimensions and connections to related problems.</abstract><doi>10.48550/arxiv.2404.16315</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs |
| title | Bounds on the dimension of lineal extensions |
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