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Proving homogenization has been a subtle issue for geometric equations due tothe discontinuity when the gradient vanishes. A sufficient condition forperiodic homogenization using perturbed correctors is suggested in theliterature [3] to overcome this difficulty. However, some noncoercive equationsdo not satisfy this condition. In this note, we prove homogenization ofgeometric equations without using perturbed correctors, and therefore weconclude homogenization for the noncoercive equations. Also, we provide a rateof periodic homogenization of coercive geometric equations by utilizing thefact that they remain coercive under perturbation. We also present an examplethat homogenizes with a rate $\Omega(\varepsilon|\log \varepsilon|)$.

Periodic homogenization of geometric equations without perturbed correctors