https://surfer.nmr.mgh.harvard.edu/ftp/articles/dale99-recon1.pdf

Cortical surface-based analysis. I. Segmentation and surface reconstruction

INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

http://www.cds.caltech.edu/%7Emurray/books/MLS/pdf/mls94-complete.pdf

A Mathematical Introduction to Robotic Manipulation

https://surfer.nmr.mgh.harvard.edu/ftp/articles/fischl99b-recon2.pdf

Cortical Surface-Based Analysis II: Inflation, Flattening, and a Surface-Based Coordinate System

We present a technique for automatically assigning a neuroanatomical label to each location on a cortical surface model based on probabilistic information estimated from a manually labeled training set. This procedure incorporates both geometric information derived from the cortical model, and neuroanatomical convention, as found in the training set. The result is a complete labeling of cortical sulci and gyri. Examples are given from two different training sets generated using different neuroanatomical conventions, illustrating the flexibility of the algorithm. The technique is shown to be comparable in accuracy to manual labeling.

/pdf/automatically-parcellating-the-human-cerebral-cortex-16g7uhc9ep.pdf

Automatically Parcellating the Human Cerebral Cortex

A method is presented for analytically calculating a smooth, three-dimensional contour about a molecule. The molecular surface envelope may be drawn on either color raster computer displays or real-time vector computer graphics systems. Molecular areas and volumes may be computed analytically from this surface representation. Unlike most previous computer graphics representations of molecules, which imitate wire models or space-filling plastic spheres, this surface shows only the atoms that are accessible to solvent. This analytical method extends the earlier dot surface numerical algorithm, which has been applied in enzymology, rational drug design, immunology, and understanding DNA base sequence recognition.

/pdf/solvent-accessible-surfaces-of-proteins-and-nucleic-acids-3euqtz86k0.pdf

Solvent-Accessible Surfaces of Proteins and Nucleic Acids

1. Curves: Parametrized Curves. 2. Regular Surfaces: Regular Surfaces Inverse Images of Regular Values. 3. Geometry of the Gauss Map: Definition of the Gauss Map and Its Fundamental Properties. 4. Intrinsic Geometry of Surfaces: Isometrics Conformal Maps. 5. Global Differential Geometry: Rigidity of the Sphere.

/pdf/differential-geometry-of-curves-and-surfaces-rsl722oix4.pdf

Differential geometry of curves and surfaces

Hypersurfaces \(M^n\)with constant mean curvature in a Riemannian manifold \(\overline{M}^{n+1}\)display many similarities with minimal hypersurfaces of \(\overline{M}^{n+1}\). They are both solutions to the variational problem of minimizing the area function for certain variations. In the first case, however, the admissible variations are only those that leave a certain volume function fixed (for precise definitions, see Sect. 2). This isoperimetric character of the variational problem associated to hypersurfaces of constant mean curvature introduces additional complications in the treatment of stability of such hypersurfaces.

Stability of Hypersurfaces of Constant Mean Curvature in Riemannian Manifolds.

Soit M n compacte, orientable, et soit x:M n →R n+1 une immersion a courbure moyenne constante non nulle. Alors x est stable si et seulement si x(M)⊂R n+1 est une sphere S n ⊂R n+1

Stability of hypersurfaces with constant mean curvature

Let \(x:{\text M}^{n}\rightarrow\,{\text R}^{n+1}\) be an immersion of an orientable, n-dimensional manifold \({\text M}^{n}\) into the euclidean space \({\text R}^{n+1}\). The condition that x has nonzero constant mean curvature H = H 0 is known to be equivalent to the fact that xis a critical point of a variational problem.

Stability of Hypersurfaces with Constant Mean Curvature

Let \(M^n\)be a compact hypersurface of a sphere with constant mean curvature H. We introduce a tensor \(\phi\) related to H and to the second fundamental form, and show that if \(|\phi|^2\leq B_{H}\), where \(B_{H}\neq 0\)is a number depending only on H and n, then either \(|\phi|^2\equiv 0\) or \(|\phi|^2\equiv{B}_{H}.\) We also characterize all \(M^n\)with \(|\phi|^2\equiv{B}_{H}.\)

/pdf/hypersurfaces-with-constant-mean-curvature-in-spheres-3sc5ueg8rn.pdf

Manfredo P. do Carmo

Papers

Differential geometry of curves and surfaces

Stability of Hypersurfaces of Constant Mean Curvature in Riemannian Manifolds.

Stability of hypersurfaces with constant mean curvature

Stability of Hypersurfaces with Constant Mean Curvature

Hypersurfaces With Constant Mean Curvature in Spheres