69 papers
This paper investigates nonconvex real-valued functions whose truncations become quasiconvex or convex beyond a certain level, with a specific focus on -smooth functions whose level sets lie within the positive definite region of their Hessian matrices, demonstrating the injectivity of their restricted gradients in that region.
This paper demonstrates that the optimal homothetic quadratic discrepancy for planar convex bodies does not necessarily follow a single order of growth, but can instead exhibit prescribed polynomial-order oscillations between logarithmic and square-root rates depending on the geometry of the boundary.
This paper introduces a novel radial and tangential decomposition framework for analyzing transient reactivity in two-dimensional linear ODEs, offering new geometric insights into state-space dynamics, orthovector structures, and the accumulation of transient amplification in nonautonomous systems.
This paper establishes that for typical self-affine sets and measures generated by contractive affine iterated function systems, the Hausdorff and box-counting dimensions of their orthogonal projections coincide and are determined by a specific pressure function, while also characterizing the conditions under which the projected measures possess exact dimensionality.
This paper establishes effective versions of Bilu's equidistribution theorem for Galois orbits of small-height points in the -dimensional algebraic torus by developing a general Fourier analysis framework that quantifies convergence rates based on the regularity of mildly regular test functions, thereby extending prior results by Petsche and D'Andrea et al.
This paper establishes that mild solutions to the incompressible Navier-Stokes equations with initial data in are weak*-continuous in time and that global solutions vanish in as time approaches infinity.
This paper establishes a comprehensive well-posedness theory for parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients, demonstrating that tempered distributions in homogeneous Hardy–Sobolev or Besov spaces serve as valid initial data for weak solutions with gradients in weighted tent spaces when source terms are of Lions' type.
This paper establishes the well-posedness and maximal regularity of weak solutions to parabolic Cauchy problems with bounded, time-independent, uniformly elliptic coefficients in weighted tent spaces by extending singular integral operator theory via off-diagonal estimates and employing interior representation techniques to prove uniqueness.
This paper proves that the fast mode dynamics in quantum operator evolution exhibit emergent random matrix universality within the Krylov space recursion method, leading to universal Green's function scaling forms in both chaotic and non-chaotic systems and enabling a new spectral bootstrap technique for approximating spectral functions.