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A dimensional mass transference principle from balls to open sets and applications to dynamical Diophantine approximation
Yubin He
The mass transference principle of Beresnevich and Velani is a powerful mechanism for determining the Hausdorff dimension/measure of sets that arise naturally in Diophant…
Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine forms with weights
Yubin He
Under a reasonable decay assumption on the approximating function, we establish a zero-full law for the Hausdorff measure of sets of inhomogeneous Dirichlet non-improvable affine f…
Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation
Yubin He
The classical Khintchine--Jarník Theorem provides elegant criteria for determining the Lebesgue measure and Hausdorff measure of sets of points approximated by rational points, whi…
A unified approach to mass transference principle and large intersection property
Yubin He
The mass transference principle, discovered by Beresnevich and Velani [Ann Math (2), 2006], is a landmark result in Diophantine approximation that allows us to obtain the Hausdorff…