Geometry, analysis, and morphogenesis: Problems and prospects
نویسندگان
چکیده
The remarkable range of biological forms in and around us, such as the undulating shape a leaf or flower garden, coils our gut, folds brain, raise number questions at interface biology, physics, mathematics. How might these shapes be predicted, how can they eventually designed? We review current understanding this problem, which brings together analysis, geometry, mechanics description morphogenesis low-dimensional objects. Starting from view that is consequence metric frustration an ambient space, we examine links between classical Nash embedding problem morphogenesis. Then, motivated by experimental observations numerical computations, revisit known rigorous results on curvature-driven patterning thin elastic films, especially asymptotic behaviors solutions (scaled) thickness becomes vanishingly small local curvature become large. Along way, discuss open problems include those mathematical modeling analysis along with driven allure being able to tame soft surfaces for applications science engineering.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2022
ISSN: ['0002-9904', '1936-881X']
DOI: https://doi.org/10.1090/bull/1765