Results 91 to 100 of about 4,692,768 (270)

On the Zoll deformations of the Kepler problem

Bulletin of the London Mathematical Society, EarlyView.
Abstract A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the potential of the harmonic oscillator. In this paper, we complement Bertrand's theorem showing the existence of an infinite‐dimensional space of central force ...
Luca Asselle, Stefano Baranzini
wiley   +1 more source

On holomorphic extension of functions on singular real hypersurfaces in ℂn

International Journal of Mathematics and Mathematical Sciences, 2001
The holomorphic extension of functions defined on a class of real hypersurfaces in ℂn with singularities is investigated. When n=2, we prove the following: every C1 function on Σ that satisfies the tangential Cauchy-Riemann equation on boundary of {(z,w)∈
Tejinder S. Neelon
doaj   +1 more source

The birational geometry of GIT quotients

Bulletin of the London Mathematical Society, EarlyView.
Abstract Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations.
Ruadhaí Dervan, Rémi Reboulet
wiley   +1 more source

Convergence of formal equivalences of hypersurfaces [PDF]

arXiv, 2000
A formal invertible equivalence between two minimal real analytic hypersurfaces converges if and only if the hypersurfaces are holomorphically ...
arxiv  

On the isoperimetric Riemannian Penrose inequality

Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.
Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri   +2 more
wiley   +1 more source

Chen-Type Inequality for Generic Submanifolds of Quaternionic Space Form and Its Application

Journal of New Theory
In 1993, the theory of Chen invariants started when Chen wrote basic inequalities for submanifolds in space forms. This inequality is called Chen’s first inequality. Afterward, many geometers studied many papers dealing with this new inequality.
Amine Yılmaz
doaj   +1 more source

Extension of holomorphic maps between real hypersurfaces of different dimension [PDF]

arXiv, 2006
It is proved that the germ of a holomorphic map from a real analytic hypersurface M in C^n into a strictly pseudoconvex compact real algebraic hypersurface M' in C^N, 1 < n < N extends holomorphically along any path on M.
arxiv  

Inequalities for the Casorati curvatures of real hypersurfaces in some Grassmannians [PDF]

, 2016
In this paper we obtain two types of optimal inequalities consisting of the normalized scalar curvature and the generalized normalized $\delta$-Casorati curvatures for real hypersurfaces of complex two-plane Grassmannians and complex hyperbolic two-plane
Kwang-soon Park
semanticscholar   +1 more source

Real hypersurfaces of a complex space form [PDF]

Proceedings - Mathematical Sciences, 2010
In this paper we are interested in obtaining a condition under which a compact real hypersurface of a complex projective space CP n is a geodesic sphere. We also study the question as to whether the characteristic vector field of a real hypersurface of the complex projective space CP
openaire   +2 more sources

Hodge loci associated with linear subspaces intersecting in codimension one

Mathematische Nachrichten, Volume 298, Issue 4, Page 1220-1229, April 2025.
Abstract Let X⊂P2k+1$X\subset \mathbf {P}^{2k+1}$ be a smooth hypersurface containing two k$k$‐dimensional linear spaces Π1,Π2$\Pi _1,\Pi _2$, such that dimΠ1∩Π2=k−1$\dim \Pi _1\cap \Pi _2=k-1$. In this paper, we study the question whether the Hodge loci NL([Π1]+λ[Π2])$\operatorname{NL}([\Pi _1]+\lambda [\Pi _2])$ and NL([Π1],[Π2])$\operatorname{NL ...
Remke Kloosterman
wiley   +1 more source