MathDB

Let

h(x,y)

be a real-valued function that is twice continuously differentiable throughout

\mathbb{R}^2

, and define

\rho (x,y)=yh_x -xh_y .

Prove or disprove: For any positive constants

d

and

r

with

d>r

, there is a circle

S

of radius

r

whose center is a distance

d

away from the origin such that the integral of

\rho

over the interior of

S

is zero.

Problem Statement