相关论文: Concerning Nikodym-type sets in 3-dimensional curv…
Within ``orbital-free'' density functional theory, it is essential to develop general kinetic energy density (KED), denoted as $t(\mathbf{r})$. This is usually done by empirical corrections and enhancements, gradient expansions, machine…
We construct supersymmetric extensions for different Skyrme-like models in 3+1 dimensions. BPS equations and BPS bounds are obtained from supersymmetry in some cases. We discuss also the emergence of several Skyrme-like models from…
Recent studies have highlighted the sensitivity of active matter to boundaries and their geometries. Here we develop a general theory for the dynamics and statistics of active particles on curved surfaces and illustrate it on two examples.…
This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can…
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding…
We establish the exact-order estimates of the best approximations of the functions from anisotropic Nikol'skii-Besov classes of several variables by entire functions in the Lebesgue spaces.
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…
By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.
We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
Until now, the only known maximal surfaces in Minkowski 3-space of finite topology with compact singular set and without branch points were either genus zero or genus one, or came from a correspondence with minimal surfaces in Euclidean…
For any integer $d \geq 2$ and prime power $q$, we construct unexpectedly large induced matchings in the point-line incidence graph of $\mathbb{F}_{q}^{d}$ by leveraging a new connection with the Furstenberg-S\'ark\"ozy problem from…
We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial segment of the curve can be continuously extended to a closed…
In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the…
We give examples of measures on certain k-surfaces in R^d. These measures satisfy convolution estimates which are nearly optimal.
I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and…
We explain how the current knowledge on the set of complete noncompact constant mean curvature surfaces can be exploited to produce new examples of compact constant mean curvature surfaces of genus greater than or equal to 3.