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T1 - Dimension estimates for Kakeya sets defined in an axiomatic setting
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UR - URN:ISBN:978-951-41-1109-9; http://hdl.handle.net/10138/176444
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A1 - Venieri, Laura
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PB - Helsingin yliopisto
Y1 - 2017
LA - eng
AB - In this dissertation we define a generalization of Kakeya sets in certain metric spaces. Kakeya sets in Euclidean spaces are sets of zero Lebesgue measure containing a segment of length one in every direction. A famous conjecture, known as Kakeya conjecture, states that the Hausdorff dimension of any Kakeya set should equal the dimension of the space. It was proved only in the plane, whereas in higher dimensions both geometric and arithmetic combinatorial methods were used to obtain partial resu...
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KW - mathematics
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