  Growing a flat lamina such as a leaf is almost impossible without some
feedback to stabilize long wavelength modes that are easy to trigger since they
are energetically cheap. Here we combine the physics of thin elastic plates
with feedback control theory to explore how a leaf can remain flat while
growing. We investigate both in-plane (metric) and out-of-plane (curvature)
growth variation and account for both local and nonlocal feedback laws. We show
that a linearized feedback theory that accounts for both spatially nonlocal and
temporally delayed effects suffices to suppress long wavelength fluctuations
effectively and explains recently observed statistical features of growth in
tobacco leaves. Our work provides a framework for understanding the regulation
of the shape of leaves and other laminar objects.
