arXiv research

Sharp bounds for Steklov eigenvalues on star-shaped domains and paraboloids.

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

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

Sharp bounds found for the first non-zero Steklov eigenvalue.

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 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.

Paper proves inequality for hyperbolic space domains.

New star-shaped acceptability indexes generalize existing methods.

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.

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.

Flow turns star-shaped curves into circles.

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.

Foliation of star-shaped polygons with fixed perimeter and area.

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.

Study classifies deformations of star-shaped curves in n-dimensional space.

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

Inverse Mean Curvature Flow bounds star-shaped surfaces' lifetime.

Inverse curvature flows shape star-shaped hypersurfaces into spheres.

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

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

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

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

The flow of symmetric spheres converges to a round sphere.

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

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…

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.

Study inverse mean curvature flow in quaternionic hyperbolic space, proving flow properties and convergence.

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 studies how shapes evolve in complex hyperbolic space.

The paper explores risk measures and arbitrage in financial markets.