Gorenstein stable log surfaces with $(K_X+\mathrm{\Lambda }{)}^2=p_g(X,\mathrm{\Lambda })-1$

In this paper, we will give a complete classification of Gorenstein stable log surfaces $(X,\mathrm{\Lambda })$ with $(K_X+\mathrm{\Lambda }{)}^2=p_g(X,\mathrm{\Lambda })-1$, where $p_g(X,\mathrm{\Lambda }):=h^0(X,K_X+\mathrm{\Lambda })$. In particular, we classify Gorenstein stable surfaces with $K_X^2=p_g-1$.