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Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary

This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical;

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Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology

oriented manifold with the structure of an A -algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's;

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Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology

oriented manifold with the structure of an A -algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's;

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An Invitation to Morse Theory

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic;

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A Short Course in Differential Topology

, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives;

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New Topological Invariants for Real and Angle Valued Maps

This book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which;

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Elements of Differential Topology

of manifold theory, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups. The first two chapters;

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Index Theory, Eta Forms, and Deligne Cohomology

a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions;

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Topological Optimization and Optimal Transport

equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless;

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The Calculus of Variations in the Large

, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with;

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Boundary Value Problems and Singular Pseudo-Differential Operators

This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral;

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Mean Curvature Flow and Isoperimetric Inequalities

evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore;

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Discrete Morse Theory

Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s;

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Introduction to Differential Geometry

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a;

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Circle-valued Morse Theory

field of contemporary mathematics with applications and connections to many geometrical problems such as Arnold's conjecture in the theory;

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Structure Of Turbulent Shear Flow

heat plumes and the atmospheric boundary layer and flows with curved streamlines. This monograph will appeal to practitioners and researchers;

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Theory of Engine Manifold Design

This book, together with its companion volume Design Techniques for Engine Manifolds - Wave Action Methods for IC Engines, reports the;

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Differential Geometry and Topology

understanding of the Morse theory. These discussions are followed by an introduction to the theory of hyperbolic systems, with emphasis on the;

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Origin of Turbulence

theory, which states all the flow instability and breakdown resulted from the gradient of the total mechanical energy normal to the flow;

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Fluid Dynamics

of this series begins with the classical theory of the boundary-layer flows, including the Blasius boundary layer on a flat plate and the Falkner;

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Topology for Computing

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields;

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Topology for Computing

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields;

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Calabi-Yau Manifolds and Related Geometries

This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate;

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SemiRiemannian Geometry The Mathematical Language of General Relativity

of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and;

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Bordered Heegaard Floer Homology

The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two;

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Dynamical Systems and Linear Algebra

. It first reviews the autonomous case for one matrix A via induced dynamical systems in {R}^d and on Grassmannian manifolds. Then the main;

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Complex Non-Kähler Geometry: Cetraro, Italy 2018

in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kahler geometry.;

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