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Results tagged with differential-topology
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user 61771
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
2
votes
Accepted
Weird claims and conclusions in "Introduction to Shape Optimization"
Not an answer, but too long for a comment. The general idea with this stuff seems to be to pair your family $\mathscr{D}$ of admissible domains with a(ny) suitable normed-space $\mathscr{V}$ of vector …
- 778
1
vote
Accepted
Prove of the shape-derivative identity relating the shape and material derivative of a shape...
The classical material derivative $D\varphi/Dt$ of a test function $\varphi \in C_c^\infty(\mathbb{R}_+\times D)$ is obtained by setting
$$
\dfrac{D\varphi}{Dt}(x) := \dfrac{\partial\tilde\varphi}{\pa …
- 778