arXiv research

Study introduces a new mean curvature flow for spherical boundaries.

New inequalities derived for hyperbolic space via specific flows.

Proves inequalities for hypersurfaces in the sphere, solving a long-standing problem.

New convexity concept applied to sphere yields quermassintegral inequalities.

The article proves inequalities for capillary hypersurfaces in hyperbolic space.

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.

We generalize Yau's estimates for the complex Monge-Ampere equation on compact manifolds in the case when the background metric is no longer Kahler. We prove $C^{\infty}$ a priori estimates for a solution of the complex Monge-Ampere equation when the background metric is Hermitian (in complex dimension two) or balanced…

Study the isoperimetric problem in Riemannian manifolds with non-trivial conformal vector fields.

Paper extends isoperimetric inequalities for non-starshaped hypersurfaces.

Researchers prove isoperimetric inequality in specific steady Ricci solitons.

The paper proves inequalities for hypersurfaces in a unit ball with specific boundary conditions.

The paper proves Michael-Simon inequalities in hyperbolic space using novel curvature flows.

Typilus predicts types for Python programs using neural networks.

LambdaNet infers TypeScript types using graph neural networks.

Study shows partially-typed NER datasets can match fully-typed ones in model performance.

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …

ptype infers data types robustly in real-world data.

Category theory generalizes finite type invariants using diagrams systems.

New spherical curve deformations solve a conjecture.

Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant changes. For example, we can significantly change a face but well-trained neural…

Finite-type surfaces have a topological Hopf property.

As entity type systems become richer and more fine-grained, we expect the number of types assigned to a given entity to increase. However, most fine-grained typing work has focused on datasets that exhibit a low degree of type multiplicity. In this paper, we consider the high-multiplicity regime inherent in data source…

Kähler-Ricci flow singularity type is independent of initial metric.

In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every $δ$(3)-ideal nul…

We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type $D$ structure by adding a "vertical" type $D$ structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type $D$ structure is that it is homotopy equivalent to a type $…

The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.

It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.

Study BF invariants using simple type concepts.

We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transver…

Study flip graphs for surfaces of infinite type, finding uncountably many connected components.

Crowdsourced labeling recovers task types with minimal queries.

Nearly Kähler and Kähler-Codazzi type manifolds are defined in a very similar way. We prove that nearly Kähler type manifolds have sense just in Hermitian and para-Hermitian contexts, and that Kähler-Codazzi type manifolds reduce to Kähler type manifolds in all the four Hermitian, para-Hermitian, Norden and product Rie…

We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…

Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.

In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore,…

Extends A-type coefficient polynomials to B-type setting, introducing new invariants.

Paper shows certain algebra types are not differentially smooth.

New representations for discrete surfaces derived from dual transforms.

Study of Lagrangian mean curvature flow with equivariant symmetry.

We study the transfer of adversarial robustness of deep neural networks between different perturbation types. While most work on adversarial examples has focused on $L_\infty$ and $L_2$-bounded perturbations, these do not capture all types of perturbations available to an adversary. The present work evaluates 32 attack…

Characterizes monodromies of projective structures on finite-type surfaces.

Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the cha…

Study covers of surfaces, showing types and properties.

New cylindrical solutions found for Grushin-type problem.

The paper estimates curvature for a specific type of equations.

In this paper, we study the Lorentzian minimal surfaces in the Minkowski space-time with finite type Gauss map. First, we obtain the classification of this type of surfaces with pointwise 1-type Gauss map. Then, we proved that there are no Lorentzian minimal surface in the Minkowski space-time with null 2-type Gauss ma…

We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister Omega_2-moves. We also show that our proof is compatible with known results for the other move types, in the sense that every knot type admits a pair of diagrams that cannot be made identical without using al…