arXiv research

Finite 2-step nilpotent groups studied by Kim and Manturov.

Study shows how to preserve Lagrangian condition in mean curvature flow on Kim-McCann metrics.

Kim-Milman flow map stable under regular target measures

Minimal generating sets found for Kim-Manturov groups.

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices and the components of dispersion matrices of multivariate normal risks for the m…

We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei, rely on maximum principles at infinity and Liouville-type theorems.

Nearly spherical, positively curved surfaces are mapped from a sphere.

We give a short proof of the following theorem of Sang-hyun Kim: if $A(Γ)$ is a right-angled Artin group with defining graph $Γ$, then $A(Γ)$ contains a hyperbolic surface subgroup if $Γ$ contains an induced subgraph $\bar{C}_n$ for some $n \geq 5$, where $\bar{C}_n$ denotes the complement graph of an $n$-cycle. Furthe…

The ideal of relations in the (small) quantum cohomology ring of the generalized flag manifold $G/B$ has been determined by B. Kim. We are going to point out a limited number of properties that, if they are satisfied by an $R[q_1,...,q_l]$-bilinear product $\circ$ on $H^*(G/B)\otimes R[q_1,...,q_l$, then the ring $(H^*…

In this paper, we consider natural geometric objects coming from Lagrangian Floer theory and mirror symmetry. Lau and Zhou showed that some of the explicit Gromov-Witten potentials computed by Cho, Hong, Kim, and Lau are essentially classical modular forms. Recent work by Zwegers and two of the authors determined modul…

We show that any two disjoint crooked planes in R^3 are leaves of a crooked foliation. This answers a question asked by Charette and Kim.

Minhyong Kim introduced arithmetic Chern-Simons invariants for totally imaginary number fields as arithmetic analogues of the Chern-Simons invariants for 3-manifolds. In this paper, we extend Kim's definition for any number field, by using the modified étale cohomology groups and fundamental groups which take real plac…

New proof shows gradient Ricci solitons with harmonic Weyl tensor have at most three eigenvalues.

Negative curvature manifolds have vanishing bounded volume class if and only if Cheeger constant is positive.

Improving a result of Eschenburg and Kim we give a criterion for semisimplicity of pseudo-Riemannian extrinsic symmetric spaces in terms of the shape operator with respect to the mean curvature vector.

A theorem of Katanaga, Saeki, Teragaito, and Yamada relates Gluck and Price twists of 4-manifolds. Using trisection diagrams, we give a purely diagrammatic proof of this theorem, and answer a question of Kim and Miller.

Geometrically reformulates the Laplace method for optimal transport.

We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local.

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the $m$-Quasi Einstein equation, but we will also call it the $(λ,n+m)$-Einstein equation. In this paper we ext…

Starting from the work of Bhupal, we extend to the contact case the Viterbo capacity and Traynor's construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.

This review deals with several microscopic (``agent-based'') models of financial markets which have been studied by economists and physicists over the last decade: Kim-Markowitz, Levy-Levy-Solomon, Cont-Bouchaud, Solomon-Weisbuch, Lux-Marchesi, Donangelo-Sneppen and Solomon-Levy-Huang. After an overview of simulation a…

New model predicts time-varying interactions in complex systems.

Infinitely many splitting spheres found for unlinked 2-spheres in 4-space.

We prove that for any winding number $m>0$ pattern $P$ and winding number $-m$ pattern $Q$, there exist knots $K$ such that the minimal genus of a cobordism between $P(K)$ and $Q(K)$ is arbitrarily large. This answers a question posed by Cochran-Harvey [CH17] and generalizes a result of Kim-Livingston [KL05].

The $c$-curvature of a complete surface with Gauss curvature close to 1 in $C^2$ norm is almost-positive (in the sense of Kim--McCann). Our proof goes by a careful case by case analysis combined with perturbation arguments from the constant curvature case, keeping track of an estimate on the closeness curvature conditi…

A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the …

Study shows exact dimensionality and regularity of manifolds for specific groups.

Friedl and Kim show any taut sutured manifold can be realized as a twisted homology product, but their proof gives no practical description of how complicated the realizing representation needs to be. We give a number of results illustrating the relationship between the topology of a taut sutured handlebody and the com…

The paper classifies vacuum static spaces with harmonic curvature.

3-balls in 4-sphere become isotopic in 5-ball.

Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.

Let K be a knot in S^3. We study the iterated Bing doubles of K, giving a new proof for the following statement: If BD_n(K) is slice for some n, then K is algebraically slice. This result was first proved by Cha and Kim using covering link calculus. We also use this tool, but our proof is substantially simpler and illu…

We introduce a new discretization of O'Hara's Möbius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under Möbius transformations of the surrounding space. The starting point for this new discretization is the cosine formula of Doyle and Schramm. We then show $Γ$-convergence…

Responding to discussions on missing data models.

Recently Auckly-Kim-Melvin-Ruberman showed that for any finite subgroup G of SO(4) there exists a contractible 4-manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G do not extend to diffeomorphisms of the entire manifold. We use a Heegaard Floer theoretic a…

In her PhD thesis Milin developed an equivariant version of the contact homology groups constructed by Eliashberg, Kim and Polterovich and used it to prove an equivariant contact non-squeezing theorem. In this article we re-obtain the same result in the setting of generating functions, starting from the homology groups…

We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface in X and an unknotted projective plane in a 4-sphere. This allows us to extend the Gabai 4-dimensional light bulb theorem and the Auckly-Ki…

We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fact they are not smoothly concordant to the positive Hopf link with a knot tied in the first component. Such examples were previously construc…

We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. W…

New findings show stabilization isn't enough for certain knotted surfaces.

Andrews and Sellers recently initiated the study of arithmetic properties of Fishburn numbers. In this paper, we prove prime power congruences for generalized Fishburn numbers. These numbers are the coefficients in the $1-q$ expansion of the Kontsevich-Zagier series $\mathscr{F}_{t}(q)$ for the torus knots $T(3,2^t)$, …

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature $σ$, then the n-iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than $2^{n-1}σ$. The same resul…

Securely analyzes survival data across multiple institutions without revealing individual patient records.

Study optimal consumption and portfolio strategies with no-borrowing constraint in financial markets.

New findings show infinitely many knots cannot be smoothly round handle slices.

Let $\mathcal{T}$ be the group of smooth concordance classes of topologically slice knots, and $\{0\}\subset\cdots\subset \mathcal{T}_{n+1}\subset\mathcal{T}_{n}\subset \cdots\subset \mathcal{T}_{0}\subset \mathcal{T}$ be the bipolar filtration. In this paper, we show that a proper collection of the knots employed by H…

Improved CNN accuracy for encrypted data using approximate activation functions.

Strong corks derived from previous work are proven.