Much has been said about bounds on Laplacian eigenvalues, and the literature can be tough to sort through! I am specifically interested in the case where the domain is a closed compact surface, and am seeking bounds on the difference between the two smallest (in magnitude) nonzero eigenvalues. Any good pointers are greatly appreciated!

Much has been said about bounds on Laplacian eigenvalues, and the literature can be tough to sort through! I am specifically interested in the case where the domain is a closed compact surface, and am seeking bounds on the difference between the two smallest (in magnitude) distinct nonzero eigenvalues. Any good pointers are greatly appreciated!