Thank you for your question about your sedge, Milla. Your plant(s) could be reacting to several environmental issues, including freezing temperatures over the last month, too much sun and high temperatures last year, and/or a lack of fertilization in early summer, 2017. These are really hardy plants, though, and you can 'mow' them to remove the ugly tips. Here is a link to an article about caring for sedge plants. In some areas, some varieties are regarded as invasive, so it may outlast you. Good luck!
Thank you for your answer! I have read the article from the link and still do not understand this phrase: You can mow the plants but use a sharp blade and mow no lower than 2/3 the plant’s height. What I should use to mow? Lawn mower? Knife?
Thank in advance, Milla
Yes; you can use a lawnmower. You just don't want to leave anything but a clean cut, which is why they recommend a sharp blade. However, if you have some pruning 'scissors,' you can use them as well. Sharpen blades, clean with alcohol (to reduce chances of infection), and snip them off. These are resilient; they'll grow back (unless it has some disease, which isn't apparent from your pictures.)