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Weakly PIC1 Manifolds with Maximal Volume Growth
In this article we study the local estimates of Ricci flow when the curvature of the initial metric is of almost PIC1 and use it to study complete...
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Pseudo-Riemannian Weakly Symmetric Manifolds of Low Dimension
We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions 2 and 3, based on the algebraic approach of such spaces...
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The \(\infty \)-Elastica Problem on a Riemannian Manifold
We consider the following problem: on any given complete Riemannian manifold ( M , g ), among all curves which have fixed length as well as fixed...
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A Survey of Topology and Geometry-Constrained Segmentation Methods in Weakly Supervised Settings
Incorporating prior knowledge into a segmentation process— whether it be geometrical constraints such as landmarks to overcome the issue of weak...
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Infinitely many solutions for elliptic equations with non-symmetric nonlinearities
We deal with the existence of infinitely many solutions for a class of elliptic problems with non-symmetric nonlinearities. Our result, which is...
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On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions
We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of...
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Maximal spacelike surfaces in a certain homogeneous Lorentzian 3-manifold
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered....
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Spectra, Group Representations and Twisted Laplacians
In this chapter, we review basic notions about spectra, group representations, and twisted Laplace operators. We first recall how to define the...
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A generalization of Stein manifolds
We define and study m - Stein manifolds which are generalizations of Stein manifolds by using m -subharmonic functions on a non-compact Kähler manifold....
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Codimension Two Spacelike Submanifolds Through a Null Hypersurface in a Lorentzian Manifold
Most important examples of null hypersurfaces in a Lorentzian manifold admit an integrable screen distribution, which determines a spacelike...
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Certain class of hypersurfaces in a Kenmotsu space forms
The purpose of this paper is to introduce of hypersurfaces in Kenmotsu space forms and study with some special conditions. In general, we have some...
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Critical Points, Compactness Conditions and Symmetric Criticality
The main aspects in nonsmooth critical point theory are discussed throughout this chapter, namely the notion of critical point for functionals which...
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Homogeneous Sub-Riemannian Manifolds Whose Normal Extremals are Orbits
In this paper, we study homogeneous sub-Riemannian manifolds whose normal extremals are the orbits of one-parameter subgroups of the group of smooth...
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Synchronisation of Weakly Coupled Oscillators
The synchronization phenomenon was reported for the first time by Christiaan Huygens, when he noticed the strange tendency of a couple of clocks to...
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On Almost Rational Finsler Metrics
We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and...
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Lorentzian connections with parallel twistor-free torsion
We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial...
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Fiberwise Symmetrizations for Variational Problems on Fibred Manifolds
We establish a framework for fiberwise symmetrization to find a lower bound of a Dirichlet-type energy functional in a variational problem on a...
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Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions
We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and...
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On the Geodesic Orbit Property for Lorentz Manifolds
The geodesic orbit property has been studied intensively for Riemannian manifolds. Geodesic orbit spaces are homogeneous and allow simplifications of...