Spacelike convex surfaces with prescribed curvature in (2+1)-Minkowski space [PDF]
, 2016 We prove existence and uniqueness of solutions to the Minkowski problem in any domain of dependence $D$ in $(2+1)$-dimensional Minkowski space, provided $D$ is contained in the future cone over a point.
Bonsante, Francesco, Seppi, Andrea
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A pinching theorem for statistical manifolds with Casorati curvatures
The Journal of Nonlinear Sciences and Applications, 2017 Summary: With a pair of conjugate connections \(\overline{\nabla}\) and \(\overline{\nabla}^*\), we derive optimal Casorati inequalities with the normalized scalar curvature on submanifolds of a statistical manifold of constant curvature.
Lee, Chul Woo +2 more
openaire +2 more sources
Rigidity and absence of line fields for meromorphic and Ahlfors islands maps
, 2010 In this note, we give an elementary proof of the absence of invariant line fields on the conical Julia set of an analytic function of one variable. This proof applies not only to rational as well as transcendental meromorphic functions (where it was ...
LASSE REMPE +10 more
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Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces [PDF]
, 2020 A well-known theorem of Wolpert shows that the Weil-Petersson symplectic form on Teichm\"uller space, computed on two infinitesimal twists along simple closed geodesics on a fixed hyperbolic surface, equals the sum of the cosines of the intersection ...
Fillastre, François, Seppi, Andrea
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On the umbilic set of immersed surfaces in three-dimensional space forms
, 2019 We prove that under some assumptions on the mean curvature the set of umbilical points of an immersed surface in a $3$-dimensional space form has positive measure. In case of an immersed sphere our result can be seen as a generalization of the celebrated
Catino, Giovanni +2 more
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Global minimizers for axisymmetric multiphase membranes [PDF]
, 2012 We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes.
Choksi, Rustum +2 more
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On the Toda Lattice Equation with Self-Consistent Sources
, 2005 The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda ...
Leon J +14 more
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Green's Function in Some Contributions of 19th Century Mathematicians [PDF]
, 2001 Many questions in mathematical physics lead to a solution in terms of a harmonic function in a closed region with given continuous boundary values. This problem is known as Dirichlet's problem, whose solution is based on an existence principle—the so ...
Rossana Tazzioli +32 more
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Curvature Pinching Conditions in Quaternionic Manifolds Under Quarter-Symmetric Metric Connections
AxiomsThis work presents a pair of sharp geometric inequalities that connect the normalized scalar curvature with the generalized normalized δ-Casorati curvature for θ-slant submanifolds immersed in quaternionic space forms endowed with a quarter-symmetric ...
Md Aquib, Ibrahim Al-Dayel
doaj +1 more source
Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds
Mathematics, 2019 Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R ×
Aliya Naaz Siddiqui +2 more
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