Submanifolds of Euclidean space with parallel mean curvature vector by Tahsin Ghazal, Sharief Deshmukh

“…First we prove that there does not exist an n-dimensional compact simply connected totally real submanifold in R2n whose mean curvature vector is parallel. Then we show that the n-dimensional compact totally real submanifolds of constant curvature and parallel mean curvature in R2n are flat. …”
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Critical Phenomena in Higher Curvature Charged AdS Black Holes by Arindam Lala

“…In this paper, we have studied the critical phenomena in higher curvature charged AdS black holes. We have considered Lovelock-Born-Infeld-AdS black hole as an example. …”
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A remark on the metric dimension in Riemannian manifolds of constant curvature by Shiva Heidarkhani Gilani, Reza Mirzaie, Ebrahim Vatandoost

“…We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V|-1$.…”
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Effect of Curvature-Dependent Surface Elasticity on the Flexural Properties of Nanowire by Mengjun Wu, Quan Yuan, Honglin Li, Bin Wu, Lin Fang, Mengyang Huang

“…., to capture the influence of surface curvature on the flexural rigidity of nanowire with rectangular cross section. …”
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Detecting phase transitions in collective behavior using manifold's curvature by Kelum Gajamannage, Erik M. Bollt

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Non-linear equation of motion for higher curvature semiclassical gravity by Naman Kumar

Subjects: “…Higher curvature gravity…”
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Spontaneous curvature in two-dimensional van der Waals heterostructures by Yuxiang Gao, Fenglin Deng, Ri He, Zhicheng Zhong

“…In this paper, we predict that 2D interfaces undergo “spontaneous curvature”, which means when two flat 2D layers approach each other, they inevitably experience out-of-plane curvature. …”
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Rigidity of Complete Gradient Shrinkers with Pointwise Pinching Riemannian Curvature by Yawei Chu, Dehe Li, Jundong Zhou

“…In this paper, we study the rigidity of Mn,g,f with pointwise pinching curvature and obtain some rigidity results. In particular, we prove that every n-dimensional gradient shrinking Ricci soliton Mn,g,f is isometric to ℝn or a finite quotient of Sn under some pointwise pinching curvature condition. …”
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Construct α′ corrected or loop corrected solutions without curvature singularities by Peng Wang, Houwen Wu, Haitang Yang, Shuxuan Ying

“…Abstract For the bosonic gravi-dilaton system, we provide systematical approaches to construct non-perturbative string cosmological solutions without curvature singularities, which can match the perturbative solution to any order in α′ expansion. …”
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A Comparison Principle for the Mean Curvature Flow Equation with Discontinuous Coefficients by Cecilia De Zan, Pierpaolo Soravia

“…We study the level set equation in a bounded domain when the velocity of the interface is given by the mean curvature plus a discontinuous velocity. We prove a comparison principle for the initial-boundary value problem whose consequence is uniqueness of continuous solutions and well- posedness of the level set method.…”
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Periodic Solutions for a Prescribed Mean Curvature Equation with Multiple Delays by Shiping Lu, Ming Lu

“…We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation (d/dt)(x'(t)/1+x't2) +∑i=1naitgxt-τit=pt. …”
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Manipulation by magnetic frustration in ferrotoroidal spin chains via curvature and torsion by Oleksandr V. Pylypovskyi, Enrico Di Benedetto, Carmine Ortix, Denys Makarov

“…A constant torsion along the chain results in alternating regions of high and low curvature, facilitating the spin spiral state perturbed by the (anti)periodic boundary conditions on the magnetic order parameter. …”
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Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions by Pat Piperni, Maahi M. Talukder

“…This new operator retains the strong smoothing properties of the Laplacian without the latter’s adverse curvature effects. However, the new operator exhibits slower convergence properties than the Laplacian, which can lead to increased turnaround times and in some cases preclude the achievement of convergence to machine accuracy. …”
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Compact Spacelike Hypersurfaces with Constant Mean Curvature in the Antide Sitter Space by Henrique F. de Lima, Joseilson R. de Lima

“…We obtain a height estimate concerning to a compact spacelike hypersurface Σn immersed with constant mean curvature H in the anti-de Sitter space ℍ1n+1, when its boundary ∂Σ is contained into an umbilical spacelike hypersurface of this spacetime which is isometric to the hyperbolic space ℍn. …”
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Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint by P. Li, T.M. Laleg‐Kirati

“…Abstract The authors propose an adaptive, general and data‐driven curvature penalty for signal denoising via the Schrödinge operator. …”
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Lightlike Submanifolds of a Semi-Riemannian Manifold of Quasi-Constant Curvature by D. H. Jin, J. W. Lee

“…We study the geometry of lightlike submanifolds (𝑀,𝑔,𝑆(𝑇𝑀),𝑆(𝑇𝑀⟂)) of a semi-Riemannian manifold (𝑀,̃𝑔) of quasiconstant curvature subject to the following conditions: (1) the curvature vector field ζ of 𝑀 is tangent to 𝑀, (2) the screen distribution 𝑆(𝑇𝑀) of 𝑀 is totally geodesic in 𝑀, and (3) the coscreen distribution 𝑆(𝑇𝑀⟂) of 𝑀 is a conformal Killing distribution.…”
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Curvature Determination Method for Diverging Acoustic Lens of Underwater Acoustic Transducer by Minze Li, Mingzhen Xin, Fanlin Yang, Yu Luo, Jinpeng Liu, Niuniu Wu

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Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection by Mohd Aslam, Mohd Danish Siddiqi, Aliya Naaz Siddiqui

Subjects: “…Normalized scalar curvature…”
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Spacelike hypersurfaces in de Sitter space with constant higher-order mean curvature by Kairen Cai, Huiqun Xu

“…It is shown that a compact connected hypersurface with positive constant higher-order mean curvature Hr for some fixed r , 1≤r≤n, immersed in the de Sitter space S1n+1 must be a sphere.…”
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Existence of Solutions for the Discrete Dirichlet Problem Involving p-Mean Curvature Operator by Jianxia Wang, Zhan Zhou

“…This work is to discuss the Dirichlet boundary value problem of the difference equation with p -mean curvature operator. Under some determinate growth conditions on the nonlinear term, the existence of one solution or two nontrivial solutions is obtained via variational methods and some analysis techniques. …”
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