arXiv research

Proves a generalized Minkowski inequality for starshaped domains.

We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt \cite{G} and Urbas \cite{U} on an expanding geometric curvature flow.

Proves Riemannian starshape of capacitary potential levels.

Study shows Reeb orbits on starshaped hypersurfaces grow logarithmically with period.

We study the existence of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space.

Paper extends isoperimetric inequalities for non-starshaped hypersurfaces.

The study finds starshaped compact hypersurfaces in warped products with curvature estimates.

We consider the evolution of starshaped hypersurfaces in the Euclidean space by general curvature functions. Under appropriate conditions on the curvature function, we prove the global existence and convergence of the flow to a hypersurface of prescribed curvature.

New findings on hypersurfaces with specific curvature properties in space forms.

Let $\mathcal{W}^{n}$ be the class of $C^{\infty }$ complete simply connected $n-$dimensional manifolds without conjugate points. The hyperbolic space as well as Euclidean space are good examples of such manifolds. Let $$ and let $A$ be a subset of $W$. This article aims at characterization and bu…

Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Bbb R$. For a positive function $ψ$ defined on $\bar M$, we generalized the arguments in \cite{GRW2015} and \cite{RW16}, to obtain the curvature estimates for Hessian equations $σ_k(κ)=ψ(V,ν(…

In this paper we find strictly locally convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed curvature and boundary. The main result is that if the given data admits a strictly locally convex radial graph as a subsolution, we can find a radial graph realizing the prescribed curvature and boundary. As an applicatio…

We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $\varphi(r)$. If $\varphi'(r)>0$ and $\varphi''(r)\geq 0$, we show that these flows exist for all times, remain starshaped and mean convex. Plus the positivity of $\varphi''(r)$ and …

New flow for capillary surfaces converges to spherical caps.

We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(κ)=σ\in(0, 1)$ with a prescribed asymptotic boundary $Γ$ at infinity has at least one smooth solution with uniformly bounded hyperbol…

We prove that, if $Ω\subset \mathbb{R}^n$ is an open bounded starshaped domain of class $C^2$, the constancy over $\partial Ω$ of the function $\varphi(y) = \int_0^{λ(y)} \prod_{j=1}^{n-1}[1-t κ_j(y)]\, dt$ implies that $Ω$ is a ball. Here $k_j(y)$ and $λ(y)$ denote respectively the principal curvatures and the cut v…

The paper studies a modified scalar curvature flow and proves convergence to a sphere.

Let $ψ$ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface $M$ for which $ψ$, when evaluated on $M$, coincides with the $m-$th elementary symmetric function of principal curvatures of $M$ for a given $m$? The corresponding existence and uniqueness…

We consider inverse curvature flows in hyperbolic space with starshaped initial hypersurface, driven by positive powers of a homogeneous curvature function. The solutions exist for all time and, after rescaling, converge to a sphere.

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

In [7], Guan, Ren and Wang obtained a $C^2$ a priori estimate for admissible 2-convex hypersurfaces satisfying the Weingarten curvature equation $σ_2(κ(X))=f(X, ν(X)).$ In this note, we give a simpler proof of this result, and extend it to space forms.

In this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a \emph{starshaped} potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model…

Find conditions for starshapedness of level sets in Heisenberg group.

We classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings. The nonexistence of rational homology disk smoothings is shown by symplectic geometric methods, while the existence is verified via smoothings of negative weights. In particular, it is shown th…

The study examines hypersurfaces in warped products and their properties.

We study the evolution of strictly mean-convex entire graphs over $R^n$ by Inverse Mean Curvature flow. First we establish the global existence of starshaped entire graphs with superlinear growth at infinity. The main result in this work concerns the critical case of asymptotically conical entire convex graphs. In this…

In this article, we prove an eigenvalue pinching theorem for the first eigenvalue of the Laplacian on compact hypersurfaces in a sphere. Let $(M^n,g)$ be a closed, connected and oriented Riemannian manifold isometrically immersed by $φ$ into $§^{n+1}$. Let $q>n$ and $A>0$ be some real numbers satisfying $|M|^\frac{1}{n…

In this note, we observe that if $B$ is a ball in a Euclidean space with dimension $n$, $n\geq3$, then a stable CMC hypersurface $Σ$ with free boundary in $B$ satisfies \[ nA\leq L\leq nA\left( \frac{1+\sqrt{1+4(n+1)H^2}}{2} \right)\,, \] where $L$, $A$ and $H$ denote the length of $\partial Σ$, the area of $Σ$ and the…

The paper proves new inequalities and flow properties for hypersurfaces.

Method generates intermediate domains to align source and target domains.

Aims to eliminate domain bias in authentication without domain labels.

CoDAG combines domain adaptation and generalization for unsupervised continual domain shift learning.

DCASE 2022 Task 2 tackles domain shifts in ASD for machine condition monitoring.

Extends polydisk theorem to Hartogs domains over symmetric domains.

Adaptive multi-domain learning reduces parameter count for efficient deep learning.

Recently multi-domain recommender systems have received much attention from researchers because they can solve cold-start problem as well as support for cross-selling. However, when applying into multi-domain items, although algorithms specifically addressing a single domain have many difficulties in capturing the spec…

Proposes novel losses for fine-grained categorical domain adaptation.

We address the problem of domain generalization where a decision function is learned from the data of several related domains, and the goal is to apply it on an unseen domain successfully. It is assumed that there is plenty of labeled data available in source domains (also called as training domain), but no labeled dat…

MetFA aligns source and target domains for cross-device image classification.

In this paper, we propose a simple model referred as Contradistinguisher (CTDR) for unsupervised domain adaptation whose objective is to jointly learn to contradistinguish on unlabeled target domain in a fully unsupervised manner along with prior knowledge acquired by supervised learning on an entirely different domain…

CSD learns a common component for domain generalization, outperforming existing methods.

Method learns domain-specific representations without supervision.

A new method uses normalizing flows for gradual domain adaptation.

We propose a method to infer domain-specific models such as classifiers for unseen domains, from which no data are given in the training phase, without domain semantic descriptors. When training and test distributions are different, standard supervised learning methods perform poorly. Zero-shot domain adaptation attemp…

Study shows how many domains are needed for generalization, using a new measure called domain shattering dimension.

TAROT enhances robustness and domain adaptability with domain-invariant features.

A new model for imputing missing values in time series data across domains.

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stron…