Morse function

English

Named after Marston Morse.

Morse function (plural Morse functions)

A real-valued function on a differentiable manifold such that, at each point in its domain where the function's differential is zero, the function's Hessian is nonsingular.

Some sources require also for each ${\\displaystyle t\\in \\mathbb {R} }$ that the preimage of ${\\displaystyle \\left(-\\infty ,t\\right)}$ be compact, or that the preimage of ${\\displaystyle t}$ contain at most one point with zero differential.

单词	Morse function
释义	Morse function English Etymology Named after Marston Morse. Noun Morse function (plural Morse functions) A real-valued function on a differentiable manifold such that, at each point in its domain where the function's differential is zero, the function's Hessian is nonsingular. Usage notes Some sources require also for each ${\\displaystyle t\\in \\mathbb {R} }$ that the preimage of ${\\displaystyle \\left(-\\infty ,t\\right)}$ be compact, or that the preimage of ${\\displaystyle t}$ contain at most one point with zero differential. Further reading Morse function on Wikipedia.Wikipedia
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