arXiv research

Smooth families of biholomorphisms between strongly pseudoconvex domains are shown to be smooth.

The study shows how strictly convex domains in Euclidean spaces are rigid.

We give a necessary complex geometric condition for a bounded smooth convex domain in Cn, endowed with the Kobayashi distance, to be Gromov hyperbolic. More precisely, we prove that if a smooth bounded convex domain contains an analytic disk in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi di…

Method approximates Lipschitz domains with smoother shapes.

Estimates time-varying network connections using multi-stage smoothing.

Diffusion models adapt to data geometry through log-domain smoothing.

New approach to solving minimal surface system Dirichlet problem on smooth domains.

Boundary of fiber convex domains is a cohomological sphere.

Corners can be identified by a drum's sound spectrum.

Paper solves a complex equation for smooth domains.

In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing an extension operator and computing its operator norm. We also present some examples of estimating the embedding constant for certain domai…

We deliver examples of non-Gromov hyperbolic tube domains with convex bases (equipped with the Kobayashi distance). This is shown by providing a criterion on non-Gromov hyperbolicity of (non-smooth) domains.The results show the similarity of geometry of the bases of non-Gromov hyperbolic tube domains with the geometry …

The paper improves generalization bounds for domain adaptation.

The study proves Gromov hyperbolicity for certain complex domains.

New constraints rule out some optimal domains for helicity maximisation.

A simple proof shows standard billiard for certain convex domains.

Smoothly bounded domains have special functions that are plurisubharmonic.

We construct open domains in Euclidean 3-space which do not admit complete properly immersed minimal surfaces with an annular end. These domains can not be smooth by a recent result of Martin and Morales

Paper improves privacy and utility of SGD with bounded domain and smooth losses.

Recent unsupervised approaches to domain adaptation primarily focus on minimizing the gap between the source and the target domains through refining the feature generator, in order to learn a better alignment between the two domains. This minimization can be achieved via a domain classifier to detect target-domain feat…

Proves a generalized Minkowski inequality for starshaped domains.

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for …

Paper improves neural network robustness certification with tighter radii estimates.

Convex domains have a unique boundary property related to normal vectors.

We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth …

For a bounded domain $Ω\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partialΩ$ can be locally represented as the graph of a continuous function. For any such domain there is a canonical smooth field of good direct…

For a given bounded domain $Ω\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as $t\to 0^+$. These coefficients (i.e., heat invariants) provide precise information for the volume of the domain $…

By means of a general gluing and conformal-deformation construction, we prove that any smooth, metrically complete Riemannian manifold with smooth boundary can be realized as a closed domain into a smooth, geodesically complete Riemannan manifold without boundary. Applications to Sobolev spaces, Nash embedding and loca…

Local vanishing theorems for complex spaces with smooth boundaries.

The paper classifies fiber structures of discontinuity domains for Anosov representations.

Criterion for lifting smooth contact maps between Carnot groups to central extensions.

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the s…

Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.

Analytic functions on specific domains are characterized by their smoothness and composites with polynomial curves.

Study shows Bergman metric is non-Einstein for certain domains.

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the present paper is to provide a short overview of some results and open problems on s…

Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous result by Loeper and Villani.

Let $p:X\rightarrow Y$ be a surjective holomorphic mapping between Kähler manifolds. Let $D$ be a bounded smooth domain in $X$ such that every generic fiber $D_y:=D\cap p^{-1}(y)$ for $y\in Y$ is a strongly pseudoconvex domain in $X_y:=p^{-1}(y)$, which admits the complete Kähler-Einstein metric. This family of Kähler-…

Paper shows regularization improves robustness in domain generalization.

In this paper, by the method of moving planes, we establish the monotonicity and symmetry properties of convex solutions for Monge-Ampere systems on bounded smooth planar domains.

Deep neural networks are susceptible to adversarial manipulations in the input domain. The extent of vulnerability has been explored intensively in cases of $\ell_p$-bounded and $\ell_p$-minimal adversarial perturbations. However, the vulnerability of DNNs to adversarial perturbations with specific statistical properti…

This paper describes a method to construct standard 4-balls from homotopy 4-balls in $\mathbb{C}^2$.

Given a smooth simply connected planar domain, the area is bounded away from zero in terms of the maximal curvature alone. We show that in higher dimensions this is not true, and for a given maximal mean curvature we provide smooth embeddings of the ball with arbitrary small volume.

Local rigidity results for Bergman and Kähler Carathéodory metrics on domains.

We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with …

Study smooth mappings between manifolds and their properties.

New BdryMatérn GP model for reliable boundary integration on irregular domains.

We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with c…