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The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional…
A recent article Li and Lv considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in certain cases where the speed is a function of a degree-one…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…
We derive and analyse an energy to model lipid raft formation on biological membranes involving a coupling between the local mean curvature and the local composition. We apply a perturbation method recently introduced by Fritz, Hobbs and…
Hypersurfaces embedded in conformal manifolds appear frequently as boundary data in boundary-value problems in cosmology and string theory. Viewed as the non-null conformal infinity of a spacetime, we consider hypersurfaces embedded in a…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
All phases of matter, solid, liquid or gas, present some excess energy, compared to their bulk, at their interfaces with other materials. This excess of energy, known as the surface energy, is a fundamental property of matter and is…
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…
We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
In this paper we formulate a geometric theory of elasticity and anelasticity for bodies containing material surfaces with their own elastic energies and distributed surface eigenstrains. Bulk elasticity is written in the language of…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
We provide a unique and novel extension of da Costa's calculation of a quantum mechanically constrained particle. This is achieved by analyzing the perturbative back reaction of the quantum confined particle's eigenstates and spectra upon…
Filaments are ubiquitous within the microscopic world. They occur frequently in both biological and industrial environments and display varied and rich dynamics. Their wide range of applications has spurred the development of a special…
We show the existence of global minimizers for a geometrically nonlinear isotropic elastic Cosserat 6-parameter shell model. The proof of the main theorem is based on the direct methods of the calculus of variations using essentially the…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including a spontaneous curvature and the conservation of surface…
Combining the intrinsic and extrinsic geometry, we generalize Einstein manifolds to Integral-Einstein (IE) submanifolds. A Takahashi-type theorem is established to characterize minimal hypersurfaces with constant scalar curvature (CSC) in…
We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical and cylindrical shapes. We evaluate…