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Euler obstruction, Brasselet number and critical points
We relate the Brasselet number of a complex analytic function-germ defined on a complex analytic set to the critical points of its real part on the...
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Critical Points of Solutions to Exterior Boundary Problems
In this article, we mainly study the critical points of solutions to the Laplace equation with Dirichlet boundary conditions in an exterior domain in...
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Upper bounds for the number of isolated critical points via the Thom–Milnor theorem
We apply the Thom–Milnor theorem to obtain the upper bounds on the amount of isolated (1) critical points of a potential generated by several fixed...
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Critical Points of Functionals
In the last section of the preceding chapter, we have already seen examples of how solutions to certain nonlinear equations could be obtained as...
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Critical Points of Potential Functions and Floer Cohomology
In this chapter, with the analysis of one-point open Gromov–Witten invariants given in the previous section at our disposal, we develop the critical...
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Multiple Critical Points of a Functional in Product Spaces with Applications to Elliptic Systems
In this paper, we deal with the existence and multiplicity of component-wise nontrivial critical points (i.e., whose components are both nonzero) for...
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Toward Computational Morse–Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points
To make progress toward better computability of Morse–Floer homology and thus enhance the applicability of Floer theory, it is essential to have...
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Critical Points for Least-Squares Estimation of Dipolar Sources in Inverse Problems for Poisson Equation
In this work, we study some aspects of the solvability of the minimization of a non-convex least-squares criterion involved in dipolar source...
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Effects of surface tension and elasticity on critical points of the Kirchhoff–Plateau problem
We introduce a modified Kirchhoff–Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic...
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Critical points of solutions to a kind of linear elliptic equations in multiply connected domains
In this paper, we mainly study the critical points and critical zero points of solutions u to a kind of linear elliptic equations with nonhomogeneous...
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Landscape Analysis for Shallow Neural Networks: Complete Classification of Critical Points for Affine Target Functions
In this paper, we analyze the landscape of the true loss of neural networks with one hidden layer and ReLU, leaky ReLU, or quadratic activation. In...
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Critical Determinant
In this chapter, we introduce the concept of critical determinant of a set in $$\mathbb...
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On the Morse index of critical points in the viscosity method
We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences of critical points...
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An adaptive high order method for finding third-order critical points of nonconvex optimization
Recently, the optimization methods for computing higher-order critical points of nonconvex problems attract growing research interest (Anandkumar...
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