Winning of inhomogeneous bad for curves
Abstract
We prove the absolute winning property of weighted simultaneous inhomogeneous badly approximable vectors on non-degenerate analytic curves. This answers a question by Beresnevich, Nesharim, and Yang. In particular, our result is an inhomogeneous version of the main result in BNY22 by Beresnevich, Nesharim, and Yang. Also, the generality of the inhomogeneous part that we considered extends the previous result in ABV. Moreover, our results even contribute to classical results, namely establishing the inhomogeneous Schmidt's conjecture in arbitrary dimensions.
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