arXiv research

The paper proves new inequalities in hyperbolic space using Euclidean methods.

This work is an extension of a result given by Kuttler and Sigillito (SIAM Rev $10$:$368-370$, $1968$) on a star-shaped bounded domain in $\mathbb{R}^2$. Let $Ω$ be a star-shaped bounded domain in a hypersurface of revolution, having smooth boundary. In this article, we obtain a sharp lower bound for all Steklov eigenv…

Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.

The paper proves inequalities for star-shaped and $F$-mean convex hypersurfaces in $\mathbb{R}^{n+1}$.

Paper develops a new method for solving IBVPs on star-shaped domains.

Let $Ω$ be a star-shaped bounded domain in $(\mathbb{S}^{n}, ds^{2})$ with smooth boundary. In this article, we give a sharp lower bound for the first non-zero eigenvalue of the Steklov eigenvalue problem in $Ω.$ This result is the generalization of a result given by Kuttler and Sigillito for a star-shaped bounded doma…

Let c be a periodic Reeb orbit on the boundary S of a compact star-shaped domain C in R4. We show that if there is an immersed symplectic disc f in C with boundary c then the self-linking number lk(c) of c equals 2 tan(f)-1 where tan(f) is the tangential self-intersection number of f. We also show that if C is convex a…

Introduces Star-Shaped deviation measures for risk analysis.

The study shows infinitely many Reeb orbits on star-shaped hypersurfaces with growth rate like prime numbers.

New star-shaped acceptability indexes generalize existing methods.

Paper proves inequality for hyperbolic space domains.

We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. Th…

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

New set-valued star-shaped risk measures introduced for better risk assessment.

Flow turns star-shaped curves into circles.

Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.

The paper studies dynamic star-shaped risk measures and their representation.

The paper characterizes dynamic return and star-shaped risk measures via BSDEs.

We consider the Laplacian with attractive Robin boundary conditions, \[ Q^Ω_αu=-Δu, \quad \dfrac{\partial u}{\partial n}=αu \text{ on } \partialΩ, \] in a class of bounded smooth domains $Ω\in\mathbb{R}^ν$; here $n$ is the outward unit normal and $α>0$ is a constant. We show that for each $j\in\mathbb{N}$ and $α\to+\in…

In this article, we introduce a new type of mean curvature flow for bounded star-shaped domains in space forms and prove its longtime existence, exponential convergence without any curvature assumption. Along this flow, the enclosed volume is a constant and the surface area evolves monotonically. Moreover, for a bounde…

The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.

The paper characterizes law-invariant star-shaped risk measures.

Introduces Star-Shaped DDPMs for non-Gaussian distributions.

The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.

Study on shape optimization for specific eigenvalue problems on domains.

In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in $\mathbf{R}^3$. We prove in this paper that this is true for the mean curvature flow of star-shaped hypersurfaces in $\mathbf{R}^{n+1}$ in arbitrary …

Paper characterizes star-shaped risk measures and their properties.

This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.

Proves a Minkowski inequality for star-shaped hypersurfaces in warped cylinders.

Inverse curvature flows shape star-shaped hypersurfaces into spheres.

Paper solves overdetermined $k$-Hessian equation in exterior domains.

Constructs Koszul dual algebras for star-shaped diagrams in 3-manifolds.

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

The flow of symmetric spheres converges to a round sphere.

Proves optimal isoperimetric inequality in de Sitter space.

Study eigenvalues for special curvature equations on star-shaped surfaces.

Study of star-shaped hypersurfaces with capillary boundary using constrained mean curvature flow.

We show that any star-shaped convex hypersurface with constant Weingarten curvature in the deSitter-Schwarzschild manifold is a sphere of symmetry. Moreover, we study an isoperimetric problem for bounded domains in the doubled Schwarzschild manifold. We prove the existence of an isoperimetric surface for any value of t…

Sharp stability of Alexandrov's theorem for $C^1$ domains in the small-excess regime

Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.

In this paper we consider a star-shaped hypersurface flow by mean curvature. Without any assumption on the convexity, we give a new proof of gradient estimate for a short time. As an application, we also give a lower bound for the blowing up time.

We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into $\RP^1$. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution …

The paper explores risk measures and arbitrage in financial markets.

Proves higher regularity for anisotropic inverse mean curvature flow.

The paper maps two types of hyperkähler manifolds and identifies their symplectic structures.

In this paper we complete the study started in [Pi2] of evolution by inverse mean curvature flow of star-shaped hypersurface in non-compact rank one symmetric spaces. We consider the evolution by inverse mean curvature flow of a closed, mean convex and star-shaped hypersurface in the quaternionic hyperbolic space. We p…

We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique cons…

We describe all families of star-shaped n-polygons in the Euclidean plane with prescribed perimeter and area ; they are leaves of a foliation F on the space of star-shaped n-polygons. By the way, we study some geometric properties of convex polygons, for instance their inscriptibility in a circle and their regularity i…